The shoulder is probably the most difficult part to rig, and poses with arms above head are especially difficult to get right when the rest pose is A-pose, because it means that the arms are far away from rest.
That said, you have probably chosen the worst pipeline from MH to Blender. Judging from the looks of the rig and the fact that you have a deltoid bone, I suppose that you have exported the Basic rig with Collada from MH 1.0.2. Even so, the deformation is extremely poor, and you should be able to get a better result by tweaking the clavicle, deltoid, and upperarm bones. However, there are several better alternatives:
Download the development version of MH and use the Default rig. It has much better deformation behavior than the old rig, still using only bones and vertex groups, no constraints or shapekeys. There used to be a nightly build but I cannot find it anymore. The source can be downloaded from https://bitbucket.org/MakeHuman/makehuman/downloads, but requires that you have python 2.7 installed.
Export the character with the MHX2 importer and import into Blender, overriding imported data and adding the MHX rig. MHX2 is a separate plugin for MH and Blender. Make sure to download the unstable version which has better deformation. It can be found at https://bitbucket.org/ThomasMakeHuman/mhx2-makehuman-exchange/downloads. Documentation is here: https://thomasmakehuman.wordpress.com/.
Here are some poses which put the shoulders to test. In the second pose I added a subsurf modifier to smooth out some wrinkles, but you probably only want that when rendering.