Yea ive done the inside of my jacket with Fabreeze there is no liner to take out. There are some pads sewn (what can i say im an idiot) into it so i dont want to wash it. However ive been riding everyday straight everywhere i go so it is getting nasty. Ill have to see if the pads on my helmet come off im not sure it is a new helmet i got this season.
Hopefully your helmet has a removeable liner, if not get one that does otherwise it will be very funky by summers end.
What is your jacket made of??? Textiles can be washed for the most part in the machine and line dryed or put the dryer on Air or Fluff with no heat. My JR mesh jacket say's don't wash but for that I'd hand wash it in the sink and again line dry it. It gets fully wet in the rain so I don't see why I can't do the same thing in a sink with soapy water.
Leather is another story if it's liner is sewn in. Maybe you should wear a long sleeve Under Armor shirt with it one to help. Otherwise stand down wind of everyone you like.
My Shoei helmet I put in the tub. I just fill it up with soapy water, dunk it, rinse it out and let it air dry. I learned this by going to their website.
My jacket I take to the dry-cleaner down the street. They do all the local AF guys from Langley's stuff, so I can trust 'em with my Jacket. They do a great job, but I don't do it only about once or twice a year. The inside I just spray with febreez to keep it de-funkified.
Helmets will dry well enough in about a day in air conditioned or heated homes. The moisture left behind will help cool you down anyway. Use a towel to squeeze the foam and soak up excess water, then let it dry.
Woolite does a pretty good job on textile jackets.