I think you have two possibilities.
If you have a profession where there is a lack of workforce and you are highly qualified, you may have a chance even without perfect knowledge of Hungarian. Fluent English will be necessary, though.
If you find a company that has strong commercial relationship with Russia, they may happy to employ someone who is native Russian.
Anyhow, it will not be easy. Try large multinational companies only. Small companies will not even answer you.
I think you will need a Visa if you want to come to the EU. I have no idea, how easy or difficult to get one.