Well, draining oil and gas starts with gas cans and a big bucket for the oil.
But first prepare your ski as if you were winterizing it.....fog the engine, shoot lube in the cylinders,etc.
Siphon the fuel out of the gas tank. If you can't get a tube into the filler neck, then remove the filler neck from behind the hull and access the top of the tank directly.
If you haven't already gotten rid of the crap grey fuel hoses, then this step will be a little harder. Remove the fuel hose at the filter, the carb and try to drain the fuel back towards the tank. If you can't, then hold a tin can under the hose in the hull to clear out the fuel. How much you do this depends on how serious much the movers about "getting out the gas".
For the oil it is a similar concept, and infinitely messier. Remove the hose to the top of the tank and siphon. In theory you could remove the straps and hoses/tubes to pull the tank completely and drain it.
I wouldn't worry about the pump oil - too small volume and not exposed the same as your fuel/oil reservoirs.
Make sure to secure the ski to the trailer with straps on the rear and check the bow strap tension. (sometimes I loosen these in storage and have to tape a note to remember to tie them down before towing).
Ask what is the best idea for the battery. I would prefer to take the battery myself and charge it before the trip and as soon as I arrived on the other side (Battery Tender!).
I would even consider building a rear bumper for the trailer out of 2x4s. This will help protect the nozzle from getting backed into things. Secure the blocking to the trailer if at all possible instead of the boat.