is there a relatively affordable way to live on a train for a few months that goes all over the country?

Buy a Pass for extended travel.
https://www.amtrak.com/take-the-trains-across-america-with-usa-rail-pass

Pack a cooler for carry on and stock it with easy to eat foods to make some meals for yourself. The train food can get expensive after a while. Many have a microwave available you can use to heat up something you have brought with you. NO you cannot use the kitchen galley to cook your own stuff.


Living ON the train is like being in a moving Hotel you are paying for each room night. You can get off the train every so often and spend a day or two enjoying the local things and stay in a cheaper place for the night.

Depending where you are going and which train you need to change to there can be a short wait for next train or maybe a days wait for the new direction.

Seriously being on a train non stop for month or more? You are taking up space and pay for it daily. You can get a reduced rate when you get a travel pass or use a discount if it applies to you.

I assume you realize that trains go from A to B. At the end of line YOU GET OFF. What you do next is up to you. Be it see the sights or get on some other train to travel some more. You DO NOT stay in the same seat for a month or two.

You used the advantage of a moving bed to avoid a hotel charge. You DO NOT get the view at night anyway.

In places with more train service like the North East in the USA you can schedule your arrival in the morning. Do your thing at the stop and then board your next ravel adventure later in the day sleeping to the next place.

Maybe for part of your extended travel you use the Bus for places the trains do not go. Just like the Airlines they have a rewards program for a frequent user.
https://www.greyhound.com/en/help-and-info/road-rewards
If you can travel at times with a companion there is a possibility of lower fares for the two of you when travelling together.

You can get an Amtrak rail pass good for 45 days of coach travel for $900. It has 18 “segments” meaning you can get on and off the train 18 times. That averages out to $20 a day which his pretty cheap when you consider you can stay on the train all night. You can take a train somewhere, stay in the place for a day and then take a night train somewhere else to avoid a hotel bill. To live cheaply have a cooler with you for food and snacks and try to avoid the dining car; that is expensive. Be aware than riding on the train you don’t need as much food as you normally eat because you are doing very little.

Of course to make this last a few months you would need two rail passes.

The best way to be able to afford living on trains for an extended length of time is to get a job working on the Railroad, stay employed until you have enough service to get a "Long Service Pass". I retired after 45 years of service as a Brakeman/Trainman, when I travel other members of the Train Crew talk to me constantly about the past and they go out of their way to help me. If there is a vacant room or roomette available they always gave it to me. Last fall I took the train from the east coast of Canada to the west coast, then I took the train to Los Angeles, then to Chicago, then to New York City and then to Montreal Quebec and back to the east coast. It cost me less than $500.

Volunteer to help clean the mess the passengers make.

No.

You're either buying tickets on Amtrak or you'd have to buy your own railcar. Very expensive. Maintain it to Amtrak standards. Very expensive. Pay railroads to pull your car wherever you want. Also very expensive.

No.
1/ No train goes all over the coutry.
2/ Staying on trains for "a few months" is going to be very expensive.

No. There are no passenger trains that go all over the country. Most passenger trains are for commuters and never leave the metropolitan area where they operate. Most long distance passenger trains just go back and forth between the same two cities repeatedly.