We have 4 air intakes on the main floor but the furnace is taking air from basement along with the odors

Is there a front vent on your furnace, closer to the fan than the vents on the first floor (of course)?

There is no vent on the front of furnace or anywhere that we can see, but it's drawing air from the furnace room as we can smell the litter box as soon as the furnace comes on

Remember air will travel the path of least resistance. Dirty filters at the return air grills will multiply the problem. But air leaks are air leaks and you need to find the sorce. Turn the blower to on at the thermostat and start checking for leaks. Use your hands to run around the system & duct work in the furnace area to see if you can feel any air movement.