I just ran into a small camp of Powder Gangers and killed them. When I was going to loot boxes, I got the "Karma lost" effect. Does this only apply to said faction or is there a "generic" karma that will make me a good or evil person of the wastes?
Karma is not faction bound. It's generic and affects everybody. So, stealing (which the game considers an "evil" act) from any faction (and any NPC, for that matter) will always cause a decrease in Karma levels.
Killing certain NPCs or members of a certain faction will either increase or decrease Karma levels depending if the NPC or faction is considered "evil" or not. e.g. Killing members of "evil" factions like Fiends or the Powder Gangers will increase karma levels and killing non-"evil" NPCs will decrease Karma levels. More info at the The Vault wiki's "FNV Karma" article.
Reputation, however, is faction bound, and has a more significant effect on gameplay.
Source: The Vault wiki, "FNV Karma" article