>>1499129good to hear that man
i suggest you buy a new chain
go kmc, any model, just for the no of speeds for your bike (7? 8?)
they're easiest to change and can be removed easily too. any other brand is fine too though
and a chain tool
i've got a park ct-5 it's pretty decent
that doesn't matter much either
when you change it, take apart the cage on your derailer that the chain goes through. Just with an allen key. It's easy. Don't touch the rest. Keep the pulleys seperate and labelled (they're different). Clean them thoroughly in kerosene, dry them, then (very minimally) dab with grease and re-assemble. Wipe off excess.
Do your best with a rag or screwdriver or toothbrush to clean the cogs
cleaning a dirty chain like that is such a bitch, and it's probably worn anyway.
A new chain will make a huge difference in smoothness. You will appreciate it. And they are very cheap online for old low-speed bikes like yours.