I use a scoop or two of Oxy Clean in with my detergent and let it soak for a day or two on many of my thrift shop quilt finds. It has really been amazing how well they clean up. If there are specific stains, you can make a paste with the Oxy on them.
I do think it is very important that your washing machine is big enough to wash and rinse the quilt well. If you are not able to use a bigger machine, I would suggest rinising multiple time to be sure to get all the dirt and soap out.