[Speedslug]

Transporting oxygen horizontally is legal as far as I know.

However you want to make absolutely certain that the oxygen tank is not rolling around by wedging it or strapping (preferred) it in place in the vehicle, that it has the steel valve cover cap screwed on over the valve properly and that you stand it up and chain it to a structure as soon as you get it home.

You will want to stand it upright and give it a few minutes before opening the valve so if there is any debris in the tank it will have a chance to settle and won't get into the valve and either clog it or cause it to get stuck open.

Another thing about oxygen tanks is the the valve stem system is kind of leaky unless it is all the way open or all the way closed. Lots of folks have lost a weeks worth of oxygen in a few hours because it all leaked out around the valve stem.

All gases and pressurized liquids can be -transported- horizontally. It is while using them that you have to pay specific attention.

CO2 is tanked as a liquid and will pour liquid out if used on its' side so it should be used upright.

Acetylene is kind of weird in that the fuel itself is stored in liquid acetone like the fizz in a soda or beer. That combined liquid is then held in a sponge like stuff within the tank. It takes a specific amount of time for the acetylene to come out of solution and if it pressure is released too fast the liquid acetone will pour out and the acetylene will come out of solution (like CO2 foam in soda or beer in a keg) and will decompress explosively in the air around you and if there is an ignition source near by you will wind up with an expanding fire ball the size of mansion i.e. Kaboom.
So you will want to stand acetylene upright for at least 3 hours but I would wait 12 hours myself.

Did anyone mention that you have to use a fuel hose marked as "T" rated for use with propane?
If you use an acetylene hose the propane will chemically attack it from the inside and you will wind up with a gummy liquid blown inside your torch which you will have to send back to the maker to get cleaned.
Also the hose can begin disintegrating and leaking propane.

And yet another thing to remember is to replace your hoses (even if you don't use them) every ten years or so. They just get old like tires and can start leaking or bulging or cracking.