I LIVE IN CALIFORNIA WANT TO VISIT FAMILY MEMBERS IN OREGON
You can always try. The TSA is accustomed to seeing people from all over the world pass security lines by flashing out their foreign passports. You could be one of them. The only problem might be though, in case you case a TSA agent that is more than half awake, the fact that your Mex passport will be issued by the L..A. consulate. That could raise a red flag (or it could not). You won't know until you actually try.
I agree with my fellow attorneys. Although you may technically be able to travel from state to state, there is definitely a real risk involved where you're stopping in places that you could be subject to inspection (airports, etc.). And, it's a risk you have to be very aware of and decide if it is worthwhile to travel when the consequences could be deportation. I generally recommend against it, but it's your choice.