There are lots of short-term cooling down tactics suggested here, but ultimately, the only solution to unbearable heat is lowering humidity, and that's where a dehumidifier or AC unit comes in.
If neither of those fixes is possible, you can shut your windows during the day, and draw your curtains/ close your blinds. At night, open all of your upstairs windows and leave all bedroom and bathroom doors open, and create a cross breeze with fans. You can also draw the air through your home by placing a fan in your window blowing air out.
It's also a good idea to avoid cooking on a normal stove or using the oven. Buy cold cuts and salad ingredients, eat sandwiches, etc, or reheat food in the microwave.
Heat rises, so consider sleeping downstairs if opening downstairs windows is an option, and also leaving your attic entrance open.
In the long term, both for your own comfort and for climate and environmental reasons, consider planting shade trees on your southern and western exposures. Creepers are another green option. The priority accorded to lawns and sunny gardens should be questioned.