My inventory is getting VERY full and and have no clue if I should keep some keys, like the 4 Tomb Keys or Phineas' Key. Should I just toss them?

It is one of the more annoying aspects of the game, the crowding of inventory. However, one of the mods allows stacking of items that didn't used to stack, so that is hugely helpful. Also, use your companions and use all of your quick-item slots and ring/jewelry type slots even if it's just bling that you can later sell. I'd keep all items that are quest related and anything that isn't obvious junk-loot for selling (gems/jewelry.)