I made a posting on another thread about this (more or less). I shall copy it below:
There are two principal routes across the DR Congo that are West to East, having done both, I can describe them here to you:
1. West to (South) East - Kinshasa to Lubumbashi (nr. Ndola, Zambia).
This is only by road (no river barges etc.) and is very difficult even in the dry season. I would never even dream of it in the wet season. (Back in the day) I assumed that this route would take me about 20 days with a 4x4. It ended up taking 2 months and countless breakdowns and repairs and contracting malaria once. Its an amazing trek if you are up for it, but with a bicycle, in short - forget it!
2. West to East - Kinshasa to Kisangani (River barge)
This is the main route across DR Congo by river. It is essentially a large barge (or several strapped together) and is pushed by a tugboat. This is an ideal method to cross DR Congo if you are on bike. It takes about 3 weeks or so (no timetable to follow as such, ask around in Kinshasa or Brazzaville). However, upon arrival in Kisangani there will be a problem - you still need to cross about 1/4 of the Congo to Uganda. The roads here are awful, but the locals use push bikes to transport palm oil in 20l jerrys (6 or so at a time!) so it is do-able. Not sure on the current regs. on entering Uganda from DR Congo (check with the embassy).
Regarding crossing from CAR to DCR:
In short - don't. There is so much corruption and crime in CAR esp. in the border areas. The chances are almost 100% that you will either be held at gun point or threatened in some way. The best way to go from West to East is as I have described above. And, with all due respect, in the event of a crisis in CAR, a bicycle is not the greatest of get-away vehicles.
All in all, sounds like a brilliant idea. This is however, not easy going by any means! Do your research (though this will only take you so far). The best method is to just get there and ask around.
This was in response to a cyclist, but you can get a 4x4 on the barge.
As for the Kisangani-Goma road, it should be do-able in the dry season, if not a bit of a slog! In the wet season - forget it!! As for the section to Kinshasa, not sure, though I very much doubt it is at all possible (within reason that is).