Typical symptoms of an open neutral. At your main panel measure between the two hots (or any 240v breaker), you should get 240v or close. Then measure between one hot and neutral at the main panel, then the other, varying loads, small space heaters make good loads since they take quite a bit of current. As you move it around and take repeated readings from both hots to neutral, document the readings. It's almost certainly a PoCo issue. This is very serious, open neutrals can do a lot of damage.
EDIT: I should have added that if you decide to do this testing, unplug all your electronics, IE cable box, routers, PCs, laptops, satellite boxes, cell phone chargers, etc. turn off breakers to your heating system, then, one circuit at a time do your testing.
ONE MORE EDIT: (sorry, still recovering from Thanksgiving dinner!) Trying to make my answer as complete and informative as possible. Counterintuative as this may seem, low voltage can be as damaging as over voltage. A motor expecting 120v and now only getting 70 (just an example), is going to over-heat, melt the insulation on the windings and die. All this sucks, but your vacuum cleaner won't anymore! Also light bulbs, esp. incandescent, that are expecting 120v but getting 160 are going to burn out in short order. I'm not sure how CFLs and LEDs respond to wide voltage variations.
AGAIN, THIS IS SERIOUS, TURN OFF EVERYTHING YOU CAN AND GET IT FIXED, MOST LIKELY A PoCo issue, maybe a failing transformer, or bad connection from the transformer to your home.