As far as carrying on the bike, I bring the 2 allen keys that fit most everything on my bike (4 and 5 mm). Much smaller and lighter than a multi-tool. When I've got the fenders mounted, then the 3 mm allen and an 8 mm open wrench would also be useful if they were to come loose. I also carry 2 tire irons, 2 tubes, a patch kit, and a fiberfix spoke with tiny spoke wrench. I always have a frame pump and my pocketknife which includes screwdrivers as well. Recently I found a need for pliers when a piece of wire got imbedded in my tire, but that piece was at such an angle that it didn't pop the tube so I rode home and used pliers. A spare chain link (try the Missing Link or a SRAM powerlink) is another good idea, though a chaintool would probably be required to remove the broken link.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72