Well, for these compos I usually think ahead of some directions I could go with the song I picked. I had a couple of directions planned for this round. Sometimes, when I hear the second source, I have an "a-ha!" moment and a new, better direction comes up in my mind. Some other times though, all the plans you had are incompatible with the song for the week, and you can't think of anything good to do with it, so for those times I just accept it will suck and roll with it.
As for inspiration, it comes and goes for me. I get periods where I can do several songs in a row and then I go for a month without doing anything new. Listening to new music brings new ideas most of the time, regardless of the genre. Sometimes I listen to a new latin jazz song and get inspiration to do a glitch hop track ¯\_(ツ)_/¯. Go figure, inspiration is just weird.
Of course, you can just be talented and put out great music without even being inspired, alas, I just hack stuff together so I gotta take advantage of inspiration when it strikes.