The world of ancient Paganism was hardly limited to the worship of the Gods. There are various other beings who were honored, and "Elf worship" was often the hardest part of Paganism for Christians to destroy. It was easy enough to substitute one God for another, but it was quite another to tell the common people that the elves which brought fertility to the land were not real!
In the various folktales and sagas we find very little which would lead us to a concrete system of what spirit was responsible for exactly what. Today, we call these various figures, who are neither mortal nor God, "Wights." We are sure of the place of the Valkyries, who were responsible for bringing the slain to Valhalla, and also for choosing who in battle would die. They seem, judging by their actions, to be supernatural beings of some type. However, Valkyries appear in various places as very human figures and their exact nature is difficult to determine. Sigrdrifa was a Valkyrie who was cursed by Odin because she refused to bring victory in battle to those whom he had chosen. Her punishment was to be married to a mortal, and the implication is clear that this would end her days as a Valkyrie. It's equally clear that she has great knowledge of the runes as she tutors Sigurd after he awakens her. In most respects she seems to be a normal human woman, although a very wise and independent one with great powers. Elsewhere, Voland and his brothers are said to have found three Valkyries sunning themselves without their swan-coats. When the brothers steal their feather-coats and hide them, the Valkyries again appear as otherwise normal women. This does not seem entirely in keeping with a supernatural origin, and it's possible that some kind of magickal order of Priestesses has become confused over time with the supernatural beings we know as Valkyries or that mortal women may somehow ascend to the position. The swan-coat seems very similar in description to Freya's falcon-coat and the entire issue may be something related to the practice of seidhr. As far as we know, the Valkyrie were not worshipped as such, but were considered more the messengers of Odin. They also serve the mead at Valhalla, and because of this whoever pours the mead into the Horn at Blot or Sumbel is today known as "the Valkyrie" (no matter what sex).
The other spirits whose place seems fairly clear are the Disir. These are spirits who are intimately linked with a family. There is also some indication that they are linked with the land, but this would be in keeping with the old ways. We forget sometimes that many landowners in Europe have been living in the same place since before this continent was discovered. The land becomes an intimate part of the family and its identity, so it is natural that family spirits would also oversee the family land. Disir are seen as women who appear at times of great trouble or change. They are somehow linked to the family bloodline, and seem most closely linked to the clanchief. There is one scene in one saga where a spirit, apparently a Dis, is passed on from one person to another who are not blood relations. However, these two friends are closer than brothers, so while the link is apparently not genetic, it is definitely familial. We know the family Disir were honored with blots at the Winter Nights and that they have great power to aid their family. As far as their origin, it's possible that they are ancestral in origin. They may be ancestors whose power was so great that they were able to continue to see to their clan. Or it's possible that the Disir are the collective spirit of the family ancestors. Freya is called the great Dis and there may be some linkage here to her position as a seidhrwoman, but the reference is sufficiently brief to remain cryptic, and open to different interpretations. We know from the sagas that Seidhr was involved with talking to various spirits (including the dead) and its possible that this is the source of Freya's name. It is also possible that she performed much the same function as a Dis to her tribe the Vanir.
Closely linked to the idea of the Disir is the Fylgia. These spirits are attached to an individual person in much the same way that the Disir are associated with a family. Fylgia usually appear either as animals or as beautiful women. They correspond to the "fetch," "totem," or "power-animal" in other cultures. Most of the time the fylgia remains hidden and absent, it is only with truly great or powerful persons that the fylgia becomes known. They may have something to do with Seidhr as well, because many sagas offer evidence of spirit travel in the shape of animals. This corresponds exactly to notions of shamanism found in other cultures.
The remaining spirits include Alvar or elves, Dokkalvar or dark elves or Dwarfs, kobolds, and landvaettir. While some have defined one being as doing one thing and another serving a different function, I'm not inclined to draw very sharp distinctions between these various creatures. They all seem "elfish" in origin, and there seems to me to be no pattern of associating one name with a specific function. We know that various landvaettir or land spirits were honored with blots. We also know that Frey is the lord of Alfheim, one of the nine worlds where the alvar are said to live.
Of all the remaining spirits, the dwarfs are the most consistent in description. We know that the dwarfs are cunning and misanthropic in character and incredible smiths, capable of creating magickal objects so valuable they are considered the greatest treasures of Asgard. Thor's hammer Mjolnir, Freya's necklace Brisingamen, and Sif's golden hair are all creations of the dwarfs. They live beneath the earth and have little to do with mankind or the Gods unless one seeks them out. What place they had in the religion we no longer know. It would seem wise to invoke them as spirits of the forge, but I can think of little other reason to disturb them.
Elves are the most difficult magickal race to pin down. Mythological sources tell us that the Alvar or light elves live in Alfheim where Frey is their Lord. However, we also have the enduring belief in folklore of the elves as faery-folk: beings associated with the natural world. These two conceptions of elves might still be linked, however, as Alfheim is known to be a place of incredible natural beauty, and Frey, their leader, is an agricultural deity. To further confuse this issue, Norse folklore has a strong belief in the Landvaettir, or land spirits who may fit into either or both of these categories. I'm inclined to lump them all together as similar beings that we simply don't know enough about to tell apart. What is important is that Asatru, like all Pagan religions, honors the natural world and the earth very deeply. Whether one calls the spirits of the land as the elves, the faeries, or the landvaettir, or uses all of these terms interchangably, respect is all important. Asatru is known for having some of the most politically "conservative" members of the modern Pagan religions, but you'll find few of us who aren't staunch environmentalists.
One of the most important spirits to honor is the house-spirit, and in fact, honoring these beings may have been a greater part of daily life than honoring the Gods. Folklore is also filled with stories of various spirits variously called faeries, elves, kobolds, brownies, tomten, etc who inhabit a house and see to its proper conduct. In the usual form of the tale, they offer to perform some housekeeping functions, but eventually turn on the owners of the house when they are insulted by overpayment. We don't have any concrete evidence for how our ancestors honored these beings, but this is not surprising because such a thing would not be a public observance and it's unlikely it would be recorded in the sagas or Eddas. We usually leave a bowl of milk out when we feel we need their help in something.
In general folklore does not paint the various elves and spirits as particularly benevolent figures. With the exception of house spirits, who as spirits of a place strongly associated with humans are bound to us on some level, they seem most interested in staying out of the dealings of mankind. There are numerous stories of people who spy upon elf women and force them to become their brides, confusingly, some of these stories are very similiar to the tales of swan maidens. Inevitably the women are unhappy and eventually escape, leaving their husbands emotionally devastated. There are also numerous stories of spirits who haunt the woods and who will drag wayward travelers into rivers to drown or to some other untimely death. When people do have dealings with the elves these beings seem to operate on an entirely different set of expectations than we do. Most of us would be gratified by the gift of a "bonus" from our employer, yet time and time again in folklore this is the easiest way to anger a house spirit. We know that elves were honored with blots, but it's just as possible that these ceremonies were made in propitiation to them rather than in kinship as are our blots made with the Gods. We suggest caution in dealing with beings with a set of values so foreign from our own. They should be approached in the same way one would approach a person from a country whose ways are very very different.
We're also very reticent to make decisions about classifying the various "other peoples." It would be very easy to draw lines and place certain spirits into little boxes which label their function, but that seems overly mechanical and of little utility. Elves and other "wights" are not human, and it might be too much to try to classify them in other than subjective terms. It's probably best to simply make your intent clear, experiment, and use the terms which work for you.
There are a whole classification of Gods which are not truly part of the Aesir, Vanir, or even the Jotnar. Wayland the Smith is the best example of this that we can offer. Wayland, called Volund in the Norse version, is the greatest of smiths, but it's clear in the mythology that he was more or less a human man. The myth tells of how he lost his wife and was enslaved by a human King. While his powers allow him to outwit and take vengeance on the king, it's clear throughout that he's not on the level of a Thor or an Odin. What one does about these demi-Gods or local Gods is a good question. I see nothing wrong with pouring a blot in their honor and dealing with them as you would any other God or Goddess. On the other hand, they are not part of the Aesir and I think it might be disrespectful to honor them with the Aesir or as part of a ceremony dedicated to the Aesir as they seem of a different nature.
Honoring ones ancestors was one of the most sacred duties of the Norsemen. One of the most important parts of greeting new people was the exchanging of personal lineages at sumbel. The worship of the Disir is closely linked to ancestor worship. However, it is difficult for modern day Pagans to seriously engage in ancestor worship. We are, for the most part, without a strong connection to our heritage, and even if we feel motivated we would probably need to skip at least a thousand years back to find ancestors who would not have been appalled by our Heathen beliefs. One substitution for ancestor worship in the modern Asatru movement has been the veneration of heros from the Sagas and legends of our people.
The manner of how we honor ancestors is also somewhat troubling. I reserve the blot ritual to Gods and other powers, and I'm not sure if it's appropriate to pour a blot to an ancestor, no matter how important he was. I think the most important part of ancestor worship is remembering, and the sumbel seems the most important part of that.
While we discuss ancestry, I must mention that some modern Asatru groups, in part because of holdovers from 19th century cultural movements, have placed a great deal of emphasis on ancestry in terms of race and ethnic heritage. Many have held that Asatru was a religion for whites or Northern Europeans only. In my not particularly humble opinion, this is pure idiocy. The basic argument for this is that people of other cultures do not share the same background and values. This is certainly true, but the key word in my opinion is culture, and all Americans by definition share a culture. Also, while I admit I would think it doubtful that people from outside of our own cultural heritage would be attracted greatly to Asatru, if they are it is for a reason and they should be welcomed and not shunned. It proves the worth of our religion and way of life that it is so strong that one would leave his own cultural path behind to take up ours.
As far as culture is concerned, the ancestry of the ancient North is alive and well in modern America. A thousand years ago settlers sailed to Iceland to avoid the growing influence of powerful kings and centralized government. This centralization of power was one of the things which Roman Christianity brought with it. Two hundred years ago, we in America rebelled against our king for much the same reasons. Our culture is much more profoundly influenced by the Vikings than most would care to admit. Our law is based on English common law, which in turn has roots in Norman and Saxon law. (Both the Saxons and Normans were descended from Germanic tribes.) Our culture is based on many of the same ideas which the Northmen held dear: the importance of the individual and the belief that individual rights outweighed collective rights. Thus, it is my assertion that we are all descended, at least in part, spiritually from the ancient Norse.