Does your land property gives you the right to anything below your property like an oil reserve? I am wondering if the state has the rights to it, or you have the rights to it in the United States. I am also wondering if you can only claim the part directly under it or it works in some other way. Also, does it make a difference if your land covers the entire oil under your land or not?
That is going to depend on the deed. In some cases a deed will include both surface rights and mineral rights. In other cases mineral rights are owned by some different entity, or by the state.
If someone else owns the mineral rights, they can exploit those without the permission of the surface owner, and in some jurisdictions at lest they have a right to come onto the property and dig or drill there, even against the surface owner's wishes. In the US that varies by state, and also by the terms of the deed.
If the surface owner also owners mineral rights, no one can dig ir drill from that land without permission, but I am not sure on the rules for 'slant digging".
Mineral rights are joined to the surface rights until they are severed.
Sometimes this is done by deed from a private owner, which shows up in the chain of title in public records.
In parts of the United States (mostly in the Rocky Mountains and places to the west of them), the United States government reserved mineral rights to itself before transferring the surface rights to private ownership.