I've read on other forums about the process of wood gasification that can provide fuel for many internal combustion engines. It might even work for the little travel devices like the bigger ones touted in the threads.

Yes if a few people set up a way to make alcohol cheap ,same as bootleggers did in 1920's , read up how some farmers , have used several mixtures that work for trucks & farm tractors etc...read up now about ways to convert from gas.

Im going old school,couple months ago i found a 1985 honda 250es big red three wheeler,part of it in a box,but i put it together got a new battery ,gased it up and it started and ran ,no smoke and real fast,hard to find parts but worth $75.00

Any type of mechanical transportation will be useful for a short period of time when it all comes to an end. Until fuel supplies run out or failures cannot be repaired.
I would prefer having a 4 legged form of transport as those are infinitely renewable, you just need 2 of them to start. And the means for upkeep which is endemic to any type of transport.
Or, a bicycle would do fairly well for travel and there are carts available to carry additional materials when using the bike. Not a lot of material but, a good sized amount of necessities when needed.
As for now, quads and dirt bikes are only usable for off-road travel being that they're not considered street legal in most areas, near as I know, and may not be legal for use in some of the off road locations. A national forest I go to hunt occasionally does not allow any type of motorized off road vehicles on any of the roads inside the forest on their dirt roads, only licensed street legal motor vehicles.
Bicycles are allowed but I do not know about horses. I think horses and riders are allowed but only in designated areas.

The latest models of Honda Quads are real quiet, built that way to be used by hunters so they may be able to drive closer to the deer herds without scattering them. There are also after market exhaust systems designed with hunters in mind that can be installed on the quad type machines. You can load them down with several hundred pounds of escape gear as long as you don't attempt to go over some steep terrain. In the country a 2 cycle dirt bike can be heard from miles away. They cannot carry much gear so what is the point in giving your position away by making all that noise? They just are not practical in a bug out or smooth move situation. The only circumstance where a dirt bike would have a tactical advantage would be to escape a city, driving around and between the traffic jammed auto's that are barely moving on the roads. Be real careful, you don't get to make any mistakes on a bike without serious injuries.

In our coming future, do you think there will be any importance in having any of the off road type vehicles? Dirt bikes or quads? I know horses play a part and are for the most part quiet whereas off road transportation is quite noisy but much faster. Any thoughts?