Grease, oils?

Just what I use:
Bike-aid brand (used to be called Dry-Slide) moly graphite lube for clutch and throttle cables.
Whatever kind of motorcycle chain lube I happen to have for the engine drive chain. (I have 4 different kinds and randomly rotate them).
Tri-Flow for the pedal chain. (Will be switching to White Lightning soon)
High temp red bearing grease for the front and rear wheel bearings, bottom bracket bearings, and transmission gears.
SolderSeal-Gunk brand white lithium grease for the clutch hub bearings.

You need to completely disassemble the wheel hubs.
You need to clean all the old grease completely out of the bearings, bearing cages, races and hubs. I use mineral spirits as a solvent and an old paint roller tray as a cleaning "tank". Old toothbrushes make for great solvent brushes.

Sheldon Brown (R.I.P.) has excellent tutorials on how to do it all.
Here's a link to his site:
Sheldon Brown-Bicycle Technical Information
In the yellow box, click "wheels". On the next page, in blue text on the left of the page, click on "Servicing Cup and Cone Hubs".

If your bike has a rear coaster brake; In the yellow box, click on "brakes". On the next page, in blue text on the left of the page, click on "Coaster Brakes".

His whole page is a precious gold mine of awesome information and very well worth the hours it takes to get familiar with it.

Edit: Here's a link to his hub overhaul page: Overhauling & Repacking Hubs

I've been using White Lightning I've heard that it was pretty good. Haven't been using it long so I can't really say how well it works. I got it at Wal-Mart of all places.

I had front bearing squeal yesterday, next thing I knew the grease was turning to oil and was all over my shoe. Took apart and replaced with high temp and seems to be good now. Temps have been in the 90s, 8 inches above the road where our bearings are at is more likely over 100 degrees. I ride to the local tavern, about 6 miles each way full throttle, no shade. Cold beer and a lap dance, doesnt get any better.

Put small dab of grease (the size of a large pea or small marble) right where the 2 gears mesh on the right side of the engine. Do not use too much or you will be cleaning grease out of your clutch very soon after.

Remove the clutch release/ sprocket cover and remove the bucking bar and bearing out of the hollow sprocket shaft. Use a pencil or something similar and pack a blob of grease inside the hollow shaft. Put the ball bearing back in the shaft, squish a little more grease in there (you can use any fresh grease that squished out when you reinstalled the bearing) and replace the bucking bar.
Wipe off any excess grease that squished out of the hollow shaft after re-installing the bucking bar so it will not make as bad of a mess behind the clutch release/ sprocket cover.
Be sure to put a dab of grease on the clutch release cam inside the release cover and a little on the tip of the bucking bar where the release cam pushes against it.

Every time I grease the transmission gears I also use the white lithium grease in an aerosol can to lube up the clutch hub bearings. Use pliers or whatever to squish the end of the red straw that comes with the can of grease to a wide, flat tip.
After removing the clutch outer plate (pressure plate) and all the friction pads, push the large clutch ring gear away from the small crankshaft pinion gear to expose as much of a gap in between the hub and ring gear as you can. The gap will be created on the opposite side of the pinion gear, towards the rear of the engine. You may even be able to see the little ball bearings in there if you use a flashlight.
I get a feel for the spray button on the can first by practicing on a piece of newspaper. You only need 2 very, very small squirts in the gap. Too much grease in the hub bearings and it will fling out and contaminate the friction pads.
Do one squirt, rotate the clutch around half way and do another squirt.
Wipe off any excess with a paper towel and brake cleaner or laquer thinner.

The ball bearing fits into the hollow shaft before the bucking bar. You have to pull out the bucking bar and typically the single bearing ball will come right out on it's own.
Sometimes a magnetic pick up tool is needed to pull an ornery ball out.
Here's a link to the clutch release guts and clutch in general:
http://motorbicycling.com/f30/animated-view-motorized-bicycle-clutch-assembly-8939.html