Hmmm... So you want to know what notes to play harmonically to a solo that you say doesn't fit in any key, at least for a long period of time? I could answer that for you, but I'm guessing your understanding of theory is small. So you probably wouldn't understand a thing I would say since it would take alot of theory to explain. To be able to give you a answer I must ask: can you write the solo out in actually music via. powertab?? do you understand what modulation is?? and how time signatures work??

Although I honestly believe if you can write a coherent solo without using scales, you should be able to think up a harmony. Truth is, there are not perfect notes. In fact, there are a group of notes/chords that can work over a certian section of a melody. It just depends on what sounds cool.