Am I able to replace these water valves on my hot water oil heater?
I suppose you could disassemble the handle and clean things but if that doesn't work then keep reading.
Sure, you can replace a ball valve yourself. Have you ever soldered (sweated) copper lines before? I'm going to guess not.
The biggest worry is in the second picture. If you go to heat up #2 for removal then you will likely heat up #1 to the point of failure.

By doing this yourself you will probably spend more money than having a professional do it since you need to buy:

Propane torch
Solder wire
Flux
Emery cloth
Soldering cloth/blanket
New ball valve

This is really a tough job for an absolute beginner to tackle as I fully expect you to ruin your new ball valve by overheating it.
Another consideration is that you need your copper line to be fully drained of water or else you won't be able to heat it properly. If you do heat it hot enough for the old solder to melt while water is in the line then you risk a small explosion because of all the steam pressure you've built up in the line itself.