I took an online class with UCLA last summer and am taking another class with them this year as well as some more at a community college. Will colleges know that I took these classes? Is there anywhere on the Common App or UC App that allows you to put in college transcripts?
Yes, there is (at least on the UC App).
The UC application and the Common App both have a place for you to list your completed college level courses. For schools that uses the Common App, you also need to send an official transcript from the college where you took the classes.