I use either Gun Scrubber or Action Blaster (degreaser), gun oil or carbon remover, a loose fitting phosphor bronze brush on a cleaning rod, some kitchen towel or rags, and a toothbrush.
Once the bolt is apart, scrub accessible areas with the toothbrush and oil, then place oil in the bolt body and scrub it with the bore brush. Once that's done, wipe off what surfaces you can and spray everything with degreaser, making sure to thoroughly flush the bolt body out with it.
When it's all clean, lightly oil accessible surfaces, then place a small amount of grease on threads, camming surfaces, and on the back of the bolt lugs. I would not place anything more than a light touch of oil as it tends to migrate out the bolt.
The other thing that really helps is a lug cleaning tool. I like the one BoreTech makes. You would be amazed at what builds up in lug recesses, especially on front locking designs such as the Mauser 98 action.
I clean quite a few pre-1945 bolts in this way and it does a great job at removing decades of fouling and congealed oil.