Trans Africa from Europe boils down to east or west side, as it's been for years.
The HU sub Sahara forum will clarify exactly what the issue is in Ethiopia.
Nail that down before you consider the east side or you may be stuck in Sudan.
Benjamin's route suggestions seem a bit convoluted, but with the right passport (not UK, US, Can, Is) to visit Iran is well worth it.
Iraq too I hear but I know of only one regionally experienced overlander who has successfully crossed the full length of Iraq from the Iran in the south to Turkey (not just nipped in to Iraqi Kurdistan).
The only way out of Iraq is to Iran, then ferry to UAE (though there is talk of KSA to Iq direct).
By far the simplest must be the freight ferry from Greece to Israel (you must fly; see my recent reply in sub Sahara forum or AMH p318).
From Is to Jordan then ferry to Sinai (assuming the direct Is-Eg border at Taba is not usable).
There is also a ferry from Tk to Lebanon from where you need to organise a Syria transit for Jordan.
See this. More complicated.
Wrt KSA: I know RTW-er Nick Sanders is currently in Dubai trying to overland KSA to Jordan for Israel, etc (he is heading back to UK).
I am not sure I know of anyone who's done this in any direction yet.
From KSA there are Red Sea ferries to Sudan and Egypt. This had been done but you need to decide on how to get around Ethiopia, if needed.
I suppose you could fly a moto Khartoum to Uganda or Kenya.
West side is same as it's been for a couple of years: ferry to Morocco (again), over Sahara (all sealed) then staying near the coast with extra borders, or winging it from Bamako to Abidjan (fewer visas).
Next hurdle is a Nigerian visa (maybe not for US?), then which way into Cameroon.
From there established route via Gabon or direct to Congo-Brazza, DRC (visa issues?) for Angola (visas less hard than they were, last I heard).
I think west side, the visa dance is a bigger issue/outright arseache than safety provided you don't get drunk in the wrong places, but it's certainly more feral than east side.
Of course the easiest option is to fly to RSA, buy a moto and roam as far north as you can/like (usually Kenya/Uganda).
But it's not a hard-won trans-Af transit ;-)