There a motley gang of bikers hanging out in Ethiopia pondering the very same question.
Plan A is to head down through Moyale to Marsabit. After the couple of bikers were stranded there for 6 days waiting for fuel when the riots first started, it seems to be pretty much back to normal. Met South African on a KTM in Addis who just came up that way. No problems to report.
Plan B, but still choice for the adventurous, is to try the Lake Turkhana route and hope that the fuel shortages have resolved enough that there is fuel at the first maybe-have-blackmarket-fuel village. No one knows at this point. Otherwise, it's hitching a ride upon arrival there and returning with fuel.
Plan C, which was investigated by a wise couple, was to fly with bike from Addis Ababa to Tanzania. A bit pricey and some disassembly and reassembly required. Backburnered for now.
I wouldn't consider southern Sudan, you would be avoiding potential tension in a previously stable country (Kenya) to travel in a known unstable region. Not a lot of people are flocking to southern sudan as their go to option
We ran in a Spanish pedal biker today (Jan 22) north of Arba Minch who just rode his bike up through the west side of Turkhana. Drastic fuel shortages reported on the west side of the lake. He was lucky to get enough fuel for his stove in Lodwar after a week of searching the towns on the way up. There is also the warning of drifting bandits in the area north of Lodwar. Plus, the age old debate of whether you can actually get a boat big enough to carry your bike across and not sink is still raging. Applicatons for the first guinea pig to try it are being still being accepted.
How to get over to Uganda is an issue still. The hotspots of Eldoret and Kisumu are a question so it would be wise to go around. Some other detour options exist as well, feel free to drop me an e-mail to discuss more.
Within a couple of weeks, there will be a few that have rode down through the two routes and there will be some updated info to post at that point