Annelida: segmental worms
The annelids form the phylum of segmented worms. Latin annellus is a ring — think "earthworm" for a sample. Not many annelids are purely aquatic in fresh water; aside from the leeches (Hirudinea), which are without bristles, the ones you'll find are all oligochaetes ("few-bristled") . They are much less important in the freshwater ecology than their multifarious marine cousins, the polychaetes ("multi-bristled"), are in marine environments. All the oligochaete worms are hermaphrodites. Some are on the edge of microscopic, as small as 1 mm. At that scale you might mistake them for nematodes.
You're already familiar with some of the four prominent families of freshwater annelids. (I'll leave out four other, less prominent aquatic families, including the few species of Eiseniella, the tiny aquatic relatives of the earthworm, representing the mostly non-aquatic family of lumbricids.)
First, the tubificids include the many species of the genus Tubifex and its close relatives. Then the lumbriculids are the blackworms: though there are only three species of lumbriculids in North America, and only two of those at all common, one of them is Lumbriculus variegatus, the familiar California blackworm, which you'll mostly think of in terms of live food. The other, Stylodrilus heringianus, is an indicator species for unpolluted water.
In marginal mudbanks you'd expect to find a third family of annelid worms, the enchytraeids, familiar to fishkeepers both as whiteworms and those miniature whiteworms called Grindal worms, all cultivated for live food.
A fourth family, the naidid worms, are probably less familiar to the average aquarist, but one web biology page remarks that Naididae and Tubificidae form 80% to 100% of the segmented worm communities in the sediments of most streams and lakes. Their major predators are fish and insect larvae.
Getting oxygen. All these segmented worms respire through their skin. Some have rudimentary interior gills and constantly gulp water. Yet some oligochaetes, tubificids and lumbriculids for example, can tolerate hypoxic, even for periods of time, anoxic conditions. Where oxygen levels drop in natural waters, tubificids come to predominate in the worm community, but they don't live where toxic byproducts of anaerobic bacteria accumulate. Instead of suffocating and dying in your gravel, the tubificids stand on their heads to swallow organic detritus and digest its microflora, while they wave their rear segments in the open water and maximize the oxygen they get by simple diffusion. Their reddish color derives from a red blood pigment that acts like hemoglobin to carry oxygen extracted from even quite low levels in the water.
The lumbriculids won't suffocate either, as long as they are in water shallow enough that they can extend their rear segments along the water surface to get their oxygen directly from the atmosphere. Lumbriculids tend to predominate in green algal detritus along marshy shores.
Links. Richard Torrens, "Freshwater worms" offers a brief sketch. An overview of the roles of annelid worms in freshwater, perhaps all you'd need to know, is at the freshwater benthos site