You could email the hotel and ask about leaving your bag there.

You should be OK on the tube provided you can lift/handle the bag yourself - you won't get much sympathy from fellow travellers and there aren't many staff around (and i'm not sure they'd help you anyway). Storage space won't be an issue.

The stations generally have lifts or escalators so you won't need to haul your bag up stairs. I think you'd probably be better off getting off at Bond Street as Oxford Circus Station is a bit of a maze and tends to be quite crowded all the time (you frequently have to use stairs to change platforms there but I'm not sure about getting to the exit).