I normally don't wipe the outside of the chain but then I didn't think I was putting any lube on there. I normally just put a drop on every link using the applicator on the top of the bottle.
Sometimes I do it just before a ride though so maybe this is the problem.
Yes, that will cause a lot of oil slop. Like he said, after letting it sit for at least 15 minutes wipe the outside of the chain as clean as you can get it. I actually use a rag dampened with mineral spirits (not soaked - just an aid in wiping). Then I do it again after the first ride or two. I rarely get appreciable oiliness on the chainstays or wheels.
As for cleaning the wheels, like others have said, there's a lot of household products that clean oiliness. Dish soap is the old generic hand cleaner used by mechanics when they run out of GoJo. I have a pump bottle on my bench of a "gritty" type of citrus based hand cleaner. It's not gritty in the sense it has abrasives in it, just a "scrubby" type of hand cleaner. I've found that works extremely well for cleaning dirt, caked/long term grime and oily grime from the bike and does not affect the finish. Squirt a little of it - a thick pasty type of stuff - on a rag, and scrub away. Maybe follow with a wet rag to wipe away residue. That said, I've only used normal household cleaners (409 type of stuff) on my rims and they get perfectly clean.