Isopropryl alchohol, wet a cloth with it and give the straps a good rub over, maybe even put some in a pot to dip a toothbrush in so you can scrub 'em. It'll dissolve all grease and grime and loosen up all the crap which should wipe off and will dry quickly.
I use it to clean the upholstery of the car when I get oily grime on it off the bike, a good scrub and you can't tell it was ever mucky.
Any mtb'er should have IPA in their tool kit, not just for disc cleaning or dot fluid spillage, but as a universal cleaner and degreaser that evaporates away with no residue and doesn't harm anything you put it on. Magical stuff!
Have a wash every day instead of bimonthly, that should help.
With IA, it has a low flash point, and gives off fumes, so beaware of naked flames and smoking near it, also be aware as its a solvent it may melt the polystyrene of your helmet.
Go to a car accessory place and pick up some of the Autoglym dry cleaning spray. It won't damage the helmet if you do manage to overspray and it'll get rid of nasty stains and whiffs.
Don't inhale it though. I spent an afternoon high as a very high thing having used it in a confined space. Entertaining but not to be recommended as a regular pass time
I wouldn't use Iso-propal alcohol though, it's melt through the polystyrene. I'd get some good old fashoined soap warm water and use some elbow grease, that should get most of the gunge out.
Just had to add that, as I knew already, but had to double check to make sure before posting it, IPA does not harm the polystyrene.
I've cleaned various bits of helmet before using it, like when I had to glue a peak onto a helmet I used it to prep the area, but the doubt was put in my head, so pulled out an old helmet, gave it a good few liberal applications of IPA, no effect on the 'styrene.
No effect after soaking, drying, then poking and tapping on it in various ways to test it's integrity. Don't forget IPA is alchohol, not trichlorethane or some other 'heavy'/'chemical' solvent, polystyrene is a plastic of sorts, when have you known a relatively harmless lchohol bother plastic?? It is quite a friendly substance which is used for medical prep on skin, would you use a heavy solvent for that?
Also, we're not talking about immersing the helmet for a prolonged period of time, we're talking possible brief contact on a tiny area when wiping the straps, it will have evaporated before any deep subsurface penetration can take place.
I agree though that you shouldn't just play about with chemicals on something as critical as a helmet, and polystyrene isn't the most resilient of materials in many ways.
I do find IPA fascinating, it is so powerful on nasty stuff such as grease/dot fluid/adhesive, etc. but is so kind to just about anything vulnerable, I havent found anything yet that it harms when you don't want it to.