I'm in TO as well and it truly is very humid. The thundershowers sure put on a show!
If you want to feel really refreshed, I'd suggest going outside and getting some cold water all over you.
But if you want to stay dry, your best bet is to drink really cold liquid and stand in front of a fan at max setting.
Had this problem for a while when I was living in one apartment. Fortunately, it was a basement apartment, so it was cooler than the rest of the building, but it was nevertheless humid enough that I could be sweaty all over by just sitting on a sofa.
In the apartment I currently am, although we do have AC, it's not the best you could hope for. There are 100 apartments in this building and because it's so ridiculously hot & humid, everybody's blasting the AC so you end up with some colder-ish air, but nothing that's quite cold enough to compensate for the weather.
Moving into a house in 1.5 weeks and it has AC as well, although I'm sure it'll be much more efficient than what we've had here.
Hang in there!