"cheapest" and "easiest" are not synonymous. the following are samples using random dates in may.
cheapest appears to be by coach from wolverhampton (via manchester) for about £34 each way, plus cost of getting yourself to/from wolverhampton.
http://coach.nationalexpress.com/ journey is overnight, about 13hr.
next (although it might depend how you choose to reach the airport, or how many days parking you need), fly birmingham to belast from about £48 each way, although depending on time of day it could be considerably more.
http://www.flybe.com/
train looks a good deal on the face of it -
http://www.seat61.com/NorthernIreland.htm - fares "from" £45.00 each way; but, using random dates I couldn't see fares of less than £80 each way from telford, but you may have better luck using your specific dates.
easiest of course is getting in your car. 240-ish miles of actual driving could be done for as little as £40 each way, depending on your car and how you drive it, but the ferry will cost you between £60 and £110 each way depending on date and time.
http://www.irishferries.com/gb/index.asp