My Passport is in the British consulate, and I would like to pick it up personally without shipping. I still have my valid Visa in my expired passport. I'm wondering if I can travel with. I also have other national IDs
No. A U.S. visa is not an acceptable ID for TSA. (And in general visas do not serve as IDs; they are to be used with a passport which is the ID.) Foreign national IDs are also not acceptable IDs.