Omegas are generally the lowest on the power level, because they are not members of a pack, of which members gradually receive symbiotic balance, power from each other.
Omegas can be the "lone wolf", one with no pack. They could have been kicked out of their pack, they could be the survivor of a pack's destruction, or they could be alone by their own choice as stated by Gerard Argent.
In Omega an unnamed man appears who turns out to be a werewolf. He was homeless, exhibited schizophrenia, his control and maturity was poor. Upon being captured by the Argents, his behaviour was totally animalistic, and they learn he is an omega. He is killed by Gerard Argent to declare war upon all werewolves of Beacon Hills.
At the start of Season 2, Scott McCall had fallen to omega status because Peter Hale, his alpha creator was killed. Subsequently, his control over his werewolf bloodlust on a following full moon in Shape-Shifted was fragile. Later, when becoming a beta as part of Derek's Pack, he had an easier time in Party Guessed.
When Peter was resurrected in Party Guessed, he was at omega status, because his alpha powers had been usurped by Derek - his power was immensely impaired and drained. In his own words, he needed a pack so to regain beta status and build his power back up again.
Also, similarly to the natural wolf, omegas could also considered the lowest ranked member in a pack but are not seen as, or accepted to be, betas by the alpha. This was the case twice with Ethan and Aiden. The twins were "the bitches" in an infamous pack before they met Deucalion, and during Season 3B when Scott refused to see them as betas of his pack because of their murderous past and wrong doing as part of the Alpha Pack though allowed them to help with the Void Kitsune.
It is possible that Derek has become an omega after giving up his alpha spark to save his sister's life as he shows no indication of having joined Scott's pack, instead choosing to work independently or with the other adults, but he also does not suffer from the reduced power and control exhibited by other omegas. He is even able to evolve into the full wolf transformation which is the highest level of power and control a werewolf can achieve. This suggests either that a powerful enough werewolf can choose to be an omega without suffering the usual consequences or that Derek has achieved a new status that goes beyond the usual alpha, beta, and omega.