I have synced songs on another computer besides the one I usually sync my iPod touch. The ones I got from the other computer won't go back to my iTunes library on my computer, but they stay on my iPod. Is there a way to put the songs on my library?

Use the search feature.
Only it knows what you will find out.

search?why search?

Ha! Why search? good question..........

Because this question has probably been answered a thousand times already and it doesn't need to be answered 1,001 times.