I would probably use mesh. Try to write down all of the mesh equations and I can check what you have. If you choose a different way (there are other ways), post that up here too so we can see.
The idea is to get as many things related to each other as you can. Then you can simplify your equations and solve for the variables.
Can I suggest you start by having a look at our DC Network Analysis section. You will then have a better understanding of the different techniques available and your questions will be more focused and relevant to the problem in the OP.
Here's what I did, not sure about it though. I used mesh current method.
I1 -> CURRENT THROUGH TOP LOOP (COUNTER-CLOCKWISE) I2 -> CURRENT THROUGH BOTTOM-LEFT LOOP (CLOCKWISE) I3 -> CURRENT THROUGH BOTTOM-RIGHT LOOP (CLOCKWISE)