I'm level 22 and don't know what to do anymore. I haven't done any DLC yet. I'm hesitant, because I don't want to miss anything important in a DLC area and not be able to get back.

In what order would you do the DLC and what if I miss anything important (a side quest, items, Skill-/SPECIAL- modifications, etc.) and have already completed the story line and am back in the Mojave? Can I re-enter the DLC areas?

I feel there is not much left to do for me in the Mojave, the base game.

Which faction did u join?
The dlcs I would do in order the first time is HH, DM, OWB, then LR. All of them u can go back to except DM.

At level 22, I don't believe u should be anywhere close to content done. I remember on Xbox before the dlcs came out of reaching lvl 30 and still having a lot to do.
Also just a heads up, if ur trying to do everything in one playthru, just a heads up u can't. Depending on ur actions and decisions, ur gonna open up quest lines and close some off.

Definitely start one of the DLCs. They add a lot of content/story, you will gain 10-15 levels by doing them.

Which DLC allows me to change a Trait? I have http://fallout.wikia.com/wiki/Logan%27s_Loophole and assume, that I need to change this before level 30.

OWB, I think. The auto-doc is said to have a re-evaluation function (once!). I've never used it though.