Some .apps only open via sudo /Applications/*.app/Content/MacOS/*
Did you perchance move your user directory? If so, I suspect what's happened is that the owner/group of those applications is not the same as "you", and that's why they work under sudo and not normally.

I had this happen to me when I got my new computer. For some reason the machine refused to use the user/group ID from the old machine, and thus I wasn't part of the user/group who had access to things. I was able to fix most of this by selecting my user folder, Get(ting) Info, and then using the gizmo at the bottom to take ownership of everything inside the folder.

I also recall that there were lingering effects elsewhere, but I don't specifically recall apps being a problem. Nevertheless, I think you want to check to see if you have write access to the various /library folders, both in your own user folder and the system folders. Just try saving a text file into the one in your user folder and see what happens.