Put them into the ground as soon as possible and water them. dig a hole and put the root ball into the hole and water. Watch closely because all the roots are in a small volume. you will have to water more often until the roots grow into a bigger volume of your soil.

why cut anything off. you paid for it and the plant grew it. tomatoes will eventually grow on all those branches.

Sounds like a 2 person job. Hopefully the pots are the cheap thin ones because at this size the best option would be cutting the pots off. I can't guarantee the plants will do spectacular but tomato plants are quite resilient. Dig your holes then have a friend steady a plant near a hole and cut the pot open. Grab the root ball and drop in the hole and fill in around it then give it a new cage or temporary support until you get the others planted if using a weave for all 3 or maybe already have a trellis up. If you are using a taller cage you might think about dropping the entire plant through the new cage roots first as to minimize damage to branches. This may take 3 people lol. Don't forget to drop a hand full of Epsom salt and time release fertilizer in the hole and work it in the soil before planting. Once planted water it in well. Hope this gives you an idea of what to do anyway. Good luck as I've never tried to transplant a tomato that big, but think it can be done.

Thank you so much, I will get everyone out there to help, and it will be easier that way.

Yes, the pots are plenty cheap and I can cut them away.

Gardendawgie, I guess there are probably different schools of thought on pruning tomatoes, but my thinking was that if I at least pinch off the suckers before making the transplant, this would give the plant fewer leaves that it has to support through the transplant process.

I got my info from a good magazine, but then found nearly the same info on this excellent blog.

Here is a link that might be useful: why and how to prune tomatoes

You can always upgrade the pot size, or move a potted plant into loose, nutritious soil, as long as you do not disturb the roots. You might have to cut the small cage away with heavy dikes. If your plant has good ventilation, it will be less inclined to fall victim to fungus. Let the foliage dry out, without withering the plant from lack of water. But after your plant has been in the ground and has established roots therein, drought resistance is greatly enhanced. Yes, in SoCal we have hot dry summers. If you are in a "wet" place perhaps you should have raised beds... Or allow for drainage, otherwise. Nothing's better than well-composted loose soil, with a heavy dose of composted horse manure.