Mania is lvl 8 xD but I am trying to do side stuff in hopes of finding enough oddities.
I've never had any difficulty at all getting to level 10 before going to the Depot, the times I played Oddity. I don't know why you're having trouble. You just need to explore more, I suspect.
Did you farm the siphoners at the Siphoner Pools for their oddity? There's at least one lootable oddity there, too.
Did you buy (or make, or steal, or disarm&keep) a bunch of traps, and go hit up the easier of the two Lunatic groups that you can get to? There should be three oddities, I think, in the map screens you "unlock" by killing off that group. And that group can be managed quite handily if you load up on bear traps, Mk 1 frag mines, caltrops, and grenades.
Did you go poke around in Junkyard and do the first two quests for both Eels and Scrappers? Great xp from doing those quests.
If you did do those quests, and decide you want to help the Eels, did you do the first few steps of the new quest line? Finding Blaine, and all that? There's some xp in that for you. If you're feeling froggy, there's no reason you can't jump all over the opportunity to wipe out the Scrappers before you go into the Depot. There's at least one oddity in the Scrappers camp, if you ddin't get it elsewhere, and man so much loot.
Did you farm cave hoppers for the three minutes it'll take to get their droppable oddity? Then give Mordre some meat (I think that's worth one Oddity xp as well, maybe?)
How about going into the three easy Depot maps and killing off the Junkyard Muties and the dogs? You might want to leave the central depot for last, since those real mutants can be a pain, but the Junkyard Muties are not hard at all. There's a bunch of Oddity xp in those three easier maps, and another huge pile of loot.
Did you go run around in the Underpassages and gank all the Lurkers? Did you go back into the GMS compound, take the caves to the east, and kill off the larger group of bandits there, with the named guy? There's so much stuff to do before you *have* to hit the Depot. You just must be skipping all of it. So, don't.