Levelling up in Multiplayer levels you up in campaign as well. As for farming Eridium, best way to do it is to find a Mechromancer online who is farming the Warrior. With Upshot the Deathtrap can just keep killing the Volcanic Rakks on the platform indefinitely, plenty of Eridium drops that way. Hell, if you're on XBL I can probably help you out on Farming up some Eridium, cash and exp, all you have to do really is log into the game and sit at your spawn while the bot does all the killing and I run around picking up the cash. Also, depending on your level, I might have a weapon or two kicking around that would help you out immensely.
Apparently I work here.....
My wife came out of the closet as a furry to me, so I Divorced her, what would you do?
"I have alot of filthy habits. Most of which I find enjoyable" -Willie Nelson as Doc Holliday