In a laboratory Petri dish, I am sure that the alcohol in the vodka would kill some or all of the bacteria, but the throat is not a Petri dish. There are many parts of the throat that vodka would not even touch. These areas would rapidly re-contaminate the non-gargled areas so any partial benefit that you might achieve would be mitigated.
Most sore throats are viral infections that only last about a week. In adults, most will improve on day three or four if you do nothing at all. I would much prefer that you gargle with saline (a weak salt water solution) than to take a chance at aspirating vodka into your lungs. This can happen and it would not be pleasant.
When you take health advice from your friends, it can either be good advice or bad. In this case, the advise was not wise. I would not recommend that you gargle with vodka.
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