Help! We moved into an old house, our plumbing vent is about 4 ft. from basement floor. Every time we use kitchen sink or bathtub, it backs up into vent pipe. Also, our sump pump backs up into vent. We have tried to snake it and also poured drain cleaner down every drain. I know the vent should be out of roof, but we have a 2 story house with attic. We rent this house. Is there a cheap and easy way to reroute vent or fix it so water doesn't keep backing up. It floods one corner of our basement and smells BAD!!

The cheapest way for you to fix this problem is to tell the landlord to fix it. This kind of repair is not your responsibility unless you have made some unusual arrangements in lieu of rent. The sump and the sewer are not supposed to be connected but apparently they are. Someone, a plumber, needs to get in there and determine how the house is plumbed and fix it. You do appear to also have some blockage in the main drain. Is there a clean out in the basement where some rodding could be done?

" Is there a cheap and easy way to reroute vent or fix it so water doesn't keep backing up?"

It's not the vent that needs attention. It's the drain line that has a partial blockage that should be snaked and cleared that needs the attention.
This is the landlords responsibility and should be addressed by him. In our area it's against code to discharge, rainwater runoff, AC condensate, water softener discharege or a sump pump into a utilities sewer system. Good luck, Tom