I like having gun cleaning patches and a paper clip or dental tools to clean out the inside channels in folding knives. I had to blunt the end of one of my dental tools for this though, because it was so sharp it poked right through the cotton patches!
I've occasionally use gun cleaning solvent (Hoppes) on grime inside folders, again using patches and a thin tool.
I seem to be getting the world's dirtiest and most blunt knives given to me to sharpen recently. A green scrub pad is nice for general cleaning, though it *will* mildly scratch steel, so only use it on blades that are already marred. To clean off rust, I've recently used a stainless steel scrubber and it worked really, really well. The green scrubbie wouldn't touch it, but the stainless took it off quickly. Bar Keepers Friend or Bon Ami is nice for more mild dirt and grime, especially on blades that are otherwise unscratched. Cleaning knives first seems like a good step, and you'll need something to do it with. What I outlined above works fairly well.
Brian.