Old oil will run out if it is mounted in a silly upside-down position. You might catch most of this with a judiciously placed ice-cream container, possible hacked about for the purpose. If you have been quick, the system should still be substantially full of oil and the pressure should show normal moments after the engine is started. Run the engine for a little while and then stop it. Please dispose of the old oil in a responsible way.
Most local councils organize free dump-stations at nominated garages.
Oil, petrol and diesel contain unpleasant chemicals. There are unanswered questions over the benzene content of unleaded petrol. Benzene is extremely carcinogenic. Whatever, it pays to minimise your contact with fuel, and with oil which will contain some fuel. Consider using barrier cream on your hands, wearing rubber gloves, and certainly washing hands after the job is done.