Well, if your speakers weren't so horribly cheap I'd say go with an amp. But, you practically don't have any speakers so you're going to need them first.
I would suggest Boston for best for the money. Also, 4 speakers will make a world of difference, especially if you're relying on the front...
Did you try that thing they call 'carpet cleaner'? They sell it in a spray can at the auto parts stores.
Bleche-White would probably work, as should regular dish detergent. You can also try the clothes detergent stain removers like Easy-Out, Shout, etc.
Oxyclean sucks.