I use picaridin lotion, it works well for me. I also treat my hiking pants/shirts/socks by soaking in permethrin. I spray permethrin on my tent and backpack. I've been in some heavily infested tick and mosquito areas and these methods seem to work well.
I’m going to second the picaridin recommendation from @SILHiker. It’s the only thing that came close to working for me when I was living in Alaska. I also used the lemon eucalyptus product as well but that definitely has an odor!
Picaridin Lotion is AMAZING. It's not oily, won't eat your clothes or gear. For me it works 100x better than DEET ever did for me. I tested it out in the 100 mile wilderness on the Appalachian Trail in the worst mosquito season ever. We had thousands (not exaggerating) surrounding us 24/7. Pants, long sleeves, and a headnet were an absolute MUST. But once I got to camp, I wanted to rinse off and put on a pair of shorts. Perfect time for a test. I slathered the lotion on my legs and propped them up on the shelter. I sat there and watched as dozens of mosquitoes swarmed around my legs. Only 2 had the nerve to land, but immediately flew back off. I spent the rest of the evening in my shorts and never got one bite. Won't hike without it now!
Another vote for picaridan. It really is a game changer for me. I’m the guy who is incredibly attractive to mosquitoes, which I find amazing because I was actually a repellent to girls in high school. Mosquitoes love me. But when I use picaridin they just won’t land. No oily, smelly, gear destroying DEET anymore.
The official word from REI: Insect Repellent Guide: Deet vs. Picardin | REI Co-op