Budget headphones

The best budget headphones are the Samson SR850. I have a pair of those. They're cheap, but sound like $200 headphones. And no, that's not a joke:

http://www.head-fi.org/t/546544/samson-sr850-superlux-oem-review-a-50-budget-champion

Might be hard to find though.

I got a pair on newest.con from a brand called eagle. They were $30 and sound really good. Really great bass for a cheap pair.

If you're dead set on $20, JVC Flats are pretty good. They are available on Amazon for $12 in some colors right now.

However, they are relatively fragile so be careful not to drop them.

You need headphones or headsets? Because what you referred are headsets, not headphones. I recommend you buying a decent ones, sadly for 20$ there is not any if you care about good quality sound, if that ones that RealNC says are really that good for 50$, buy them, 50$ is not expensive.

order some beets by bolin

I'll second the opinion, that reasonable headphones start at 50$. But then again, maybe you don't care or don't hear the difference. Just go to some place you can listen to a few models and make your own opinion.

Apart from the ones RealNC recommends, I'll add Superlux HD660 and Creative Aurvana Live.

For $20, the Monoprice headphones

If you raise your budget a bit, there are some good Superlux models available.

I'll just leave this here and let you do the reading

Koss UR-20. Cheap, sound good, isolating, HUGE cans that are completely over the ear and comfortable foreeeeever, super long and extremely durable cord. Koss has lifetime guarantees on all their headphones too.

Headsets are a ripoff never buy them, if you need a microphone just get these cheap clip ons, 3 of them for $6, its all you need.

sony mdr zx 100 or mdr zx 500 if you wish to spend 30$. you can buy these at walmart, or of off amazon. http://www.amazon.com/Sony-MDRZX100-Series-Stereo-Headphones/dp/B004WODP20/ref=sr_1_1?ie=UTF8&qid=1413163151&sr=8-1&keywords=sony+mdrzx100+zx

to be honest a friend of mine told me that he has been using a really cheap non microphone headset and with it he has this microphone:
http://www.amazon.com/gp/product/B005DJOIHE/ref=oh_aui_detailpage_o01_s00?ie=UTF8&psc=1
He said that the microphone quality is more than amazing. Just a heads up! good luck!

Tascam TH-02 are relatively recommended in this price range. I would save for Koss Porta Pro as entry level.

Superlux headphones. There is no comparison in that price range