If its Ripstop nylon. should not be a problem inside a front loader washer., With it stuffed inside a pillow case. Short hand wash warm cycle.
Depends on the water proofing used.. can still be re-applied after cleaning. Lots of spray proofing on market. Depends on construction of hammock and makers instructions on how to clean.
If its like Poison oak. The oils is the nasty critter in the plant.
Can buy technu, dump good amount in a Bucket of good warm water.. and do a good hand washing with it. Rinse, Repeat.. hang to dry.
Down or Ivry Dish soap.. WITH OUT the anti-bacterial component inside it. Is a good natural Soap. Plus, it cuts oils. Like your greasy Frying pans. Works on clothing as well. Just easy on agitation, likes to foam up. use big bucket.. Hot water, that your hands can stand.. wash.. Rinse.. Repeat.. hang to dry.
That should remove the Oil's. SHOULD..