It depends on the law of your state. In my state, Washington, the State Patrol has inspection lanes where they examine vehicles that people want to get Washington State titles on. Most of those vehicles come from out of state, and have documentation from the previous state. The inspection is to confirm that the vehicle matches the documentation and that the identification has not been altered. Occasionally they have located stolen vehicles doing the inspection.
There also are procedures for licensing/titling vehicles that have never been licensed or titled before or the documentation has been lost or is unknown. The WSP can assign a vehicle identification number, like to an assembled trailer that never had a VIN. Or they can authorize a provisional title if no records can be found after a search of various data bases. This provisional title can become a legal, regular title after a time period elapses, if a previous legal owner of the vehicle cannot be located.
I would suggest talking to your local law enforcement agency to see if they know how this problem is handled in your state. If they don't handle it themselves, they should be able to steer you in the right direction.
Another suggestion: I would not do anything to or with the trucks until you have legal paperwork that shows that they belong to you. I know of a situation where a guy did a bunch of work on, and installed a nice metal bed on an early 50's GMC that he was "given" as an abandoned vehicle left on the property of his boss. It turned out that the actual, legal owner had been in prison for a couple of years. When he got out, he saw his truck being operated by this other guy. And as it ended up, the guy who had been in prison got his truck back and the guy who had invested a couple of thousand dollars in it was just out his investment. Because he didn't handle the "abandoned" vehicle according to law and through proper procedures.
Good luck, I bet there is a way for you to get legal ownership, sanctioned by your state.