So I want to take an online college class during my senior year, but my high school says they cannot put it on my transcript because it does not grant high school credit. Will I still be able to report my grade/credits to colleges on my applications?
Yes
Not only can you report it on the application, for most colleges, you must list it.
You will report it on your application, and you will send an official copy of the transcript from that college to every place that you apply to.