Is it possible to put a Steam game onto a USB drive and have it work without a direct way to install Steam?

Almost all Steam games and applications are protected by Steam's copy protection scheme which requires that the Steam client be installed on the computer you use it on. It also requires that the client be able to connect to the Steam servers at least once to validate the game. RPG Maker VX Ace isn't exception, so no, you can't do what you're asking.

However there are a couple of possible workarounds. The first is that while the RPG Maker VX Ace application is protected by Steam DRM, games that you create with it aren't. So you can create your games at home and bring the finished result to to class to demonstrate. The second possibility is you might be able to download the RPG Make VX Ace trial directly from the RPG Maker web site. It's possible though that this also is protected by Steam or some other form of DRM, but it doesn't look like it from the description. Either way it doesn't cost you anything to find out.

(It's also possible that the full version of the application available direct from the web site isn't DRM protected, but this is much more costly to verify.)

Finally since you need access to the Steam servers for legitimate school work, there's a small outside chance you may be able to convince the powers-that-be to make an exception for you.

You could consider using a phone as a mobile hotspot - set it all up with a USB, etc. then go to school, connect the computer to your phone's mobile hotspot, and then start Steam. Once it's all loaded, close steam, turn off mobile hotspot and start steam again. Because it's done it's first verification, it should work from then on. OR you could try to get Steam to connect through a VPN, but that might be harder.

Portable hard drive running all of steams files from there. It will require the computer hove have things already on it like .net c++ directx ect for the game to run but u can download all that even the .dll files