Having oil on your clothes AFTER washing is a VERY, VERY bad sign. It often indicate that a catastrophic and fatal failure may appen at any time. :(
NEVER EVER overfill your machine!!!
If at all possible, don't fill to more than 3/4 load, idealy no more than 2/3 to be safe untill the problem is fixed.
Demmand to every body in your household to be REALY carefull with the washing machine and reduce their loading to the recommended amounts.
You may have a problem with the gear box, maybe a worn bushing or something more serious.
Call a thencitian to take a look and maybe repair the machine.
Sadly, you may need to get a new washer.
Electro, June 2014