Are you sure you saw a worn belt on your washer? The model number you provided has no drive belt. This model washer is a direct-drive system that uses a motor coupling in place of a drive belt. The most common cause of a no spin problem is either a lid switch malfunction, or a broken motor coupling. The following link explains how to diagnose the problem:
Included are parts resources (if required) and instructions on how to replace each part if needed.
As far as the oil leak is concerned, it depends on how significant the leak is. The gearcase (transmission) contains an amber colored oil. Some of this oil can leak out through a small breather hole on the top of the transmission case. If all you are getting is a small puddle that does not appear to be getting worse, you may continue to use the washer (sometimes for years) with no problems. If the leak is bad, however, it may be time to replace the gearcase. Replacing the gearcase is not a difficult task, but it can take about an hour or two for the inexperienced.
IMPORTANT: The washer needs to remain in the upright position, or you can inadvertantly drain your oil through the breather hole on top of the gearcase. It is okay to tilt the washer back as you described, but DO NOT lay it down.
The following link explains step-by-step how to replace the gearcase:http://www.fixya.com/support/r3576575-replacing_a_gearcase_on_whirlpool_manufa
Read through the link provided to see if this is a repair you feel comfortable with attempting. The average cost of a replacement gearcase is about $150. You can purchase replacements at any of the following websites:
NOTE: Sometimes Sears offers a refurbished gearcase for about half the price of a new one. It will be listed in their parts listing with an "R" after the part number is available.
The first three sites I have listed also include helpful exploded view diagrams to assist you in locating and properly identifing the parts you need. It can also assist you in determing how to assemble or disassemble your appliance. The gearcase is listed as item 9 under the "Brake, Clutch, Gearcase, Motor and Pump" heading.
My advice to you is to read through the links provided and review the symptoms for the lid switch and motor coupling first. If those parts appear to be fine, inspect the interior of the washer by removing the case so you can get a real good look at how bad the leak is. If there is an oil spray pattern all round the interior cabinet walls of the washer, its time to replace the gearcase. If the leak is just a small puddle, clean it up and place a sheet of cardboard under the washer so you can monitor how much it leaks in the future. My experience has been that its not worth the effort to attempt to remove the gearcase and try to reseal it. If you're going to go through the whole process of removing the gearcase, you it would be smarter just to replace it with a new one, rather than possibly having to repeat the process again if sealing it doesn't work.
If the gearcase is still working, does not make any loud or unusual noises and the leak does not appear to get any worse, you may still get some good use out of the washer. Please let me know if you need further assistance. I hope this helps you decide.
NOTE: Here is a view of the mechanical section of your washer, based on the model number you provided:
The motor coupling is listed as item 13. Your gearcase (transmission is listed as item 9.