>>/4759/
> Can a ghost possess something that's not technically alive and has no soul?

I have gleaned the following with a little research Re: no soul
More information from you is required:

1. You can't astral project.
2. Necrotic damage still applies
3. You cannot be raised if you cease to function.
4. Immune to "Magic Jar"
5. If your body has soul hosting capability then you can be processed. Dwarven automations are said to have the capacity to carry a soul but that soul had no will over the automation.
6. If you can be "knocked unconscious" then there must necessarily be a "conscious": a mind as complex as any humanoid.
7. You cannot be resurrected
8. No dreams
9. You may not call yourself a demon, devil or genie
10. You are excluded from certain planes such as the astral plane and negative plane.
11. There is conjecture that you would be considered undead and that does make some interesting connections but I reject it as undead implied capable of dying implies life beforehand, life always contains spirit or it would be a limited chemical reaction so you cannot be turned or become undead.
12. If your character truly possesses no soul, then it has something functionally similar; a more powerful animating spirit or complexity akin to a soul. An animating spirit is separate from the soul, this is how the body can live without the soul. 
13. Both body and soul have identical access to memories.
14. In 5e, you would be excluded from learning anything or comprehending new information.

Please State the nature of this software or hardware. What gives you the ability to learn and comprehend?

15. 5e treats the soul as the repository of all learning and memories, this is for the purpose of raise dead and resurrection so no memories are lost. 

If you do not have a brain either, then where/how are your memories stored? 

> I assume it was immune to most attacks. Can you literally beat a ghost if you try hard enough?

It is half in the astral plane and half in the material plane so it can be damaged on the material plane but it doesn't die, instead I presume it is pushed back to the astral plane.