My experience is from Christmas 2008, but have friends who have gone through recently who tell me the same still applies.
If you want a 14 day transit visa, its no worries. You must first get an Egyptian visa in Addis to prove you are moving on after Sudan (well, Egyptian providin thats the way youre headin after Sudan). Without tis they want help you.
It was 100usd for this transit visa, one form, and 2 photos.
I have also obtained a 30day tourist visa before for Sudan. This is nowhere near as easy and really you need an agent to help you out. You basically need clearance from Khartoum after they recieve a letter of invitation (this has to be from a Sudanese resident in the country). Once approved, Khartoum will fax through the approval to the embasy in Addis with a number. ou have to have this reference number, without it no way!
All in all though it is very very expensive for Brits. Including agent service fee, invitation letter, the actual visa, and then registration at the border post....wait for it.....430usdollars! Yes that expensive. You might shave 50-80us off that by going with a cheaper agent but this guy was good and efficient.
But really, unless going south to Juba and beyond, there is no need for more than 14 day transit visa.
Beware, there is a fat dude who works as security in the Sudan embassy in Addis....smokes like a chimney and coughs alot.....DO NOT get on his wrong side, he will literally throw you out by the scruff of your neck. We called hm "Bully".......keep on his good side!