What is the biggest off-road tire I can run on a 84 f150 4x4 without changing gears or having transmission problems

 

Depends on what you got. Think you have a 300. If so it will run 31s pretty easy. 33s will be a bit less power. 35s will struggle a good bit on hills. Atleast 1 lower gear.

Now with that said, a good cam and maybe p&p the head with fuel injection exhaust manifolds can put it back close to stock driving power.