When picking at it or pressing it with your tongue you cause the pus to ooze and so you notice the odour. Definitely need to see a dentist. Antibiotics are probably in order.
Using hydrogen peroxide as a rinse for extended periods has been linked to increasing the risk of oral cancer especially if you are a smoker and/or drinker. You are best to use the peroxide on a Qtip and gently dab it over the area as a TEMPORARY measure.

I just got my wisdom teeth out and there is a strange smell coming from the hole where my bottom left tooth used to be. It's utterly repulsive if I do say so myself

I hope you are gently rinsing with warm salt water.

Im 20 and I have the same problem. Im thinking my dad had the same problem because my wisdom tooth smells exactly like my dad's bad breath. Although there is no pain at all... the smell is really bothering me. I never knew how serious th is problem can be. I noticed this problem for the past 6 months now, should I immediately see a dentist or can I just wash my mouth with Listerine and salt water for a few weeks and see how it is?

I'd definitely go see a dentist. You want to be sure there is no infection in your mouth.

After brushing your teeth, use salt water (mix a spoon of sea salt with 25 ml water) in a period of one or two weeks, you will see and feel the difference. Have the salt water in your month for 2-3 min (ensure the water reachs your wisdom tooth). Then clean your teeth by using dental floss.

Do it twice a day if the smell is so bad :D. Believe me, salt water is better than any other medicines/mouth wash... Let me know the result! Good luck :D

I too know this problem, also finding lack of finances a huge hindrance in getting help!
Have seen an oral surgeon who was happy to remove but I simply could not afford, now going back to dentist for a deep scale/clean... hoping for a miracle??

Oh boy I can relate... having being diagnosed with an impacted wisdom [lower] almost 18 months ago, still trying to locate a surgeon who is affordable? Have fought the "smell" with just about everything, nothing lasts and using a mouthwash for too long can have its own risks!
I was quoted close to $1,100 to have this thing removed, but not able to come up with this kind of money?
So, while I try to figure this out, have opted to return to my dentist for a deep scale/clean, with a hope she is able to think of another alternative... good luck!