You can find some very good earphones under $20.
Clip ons: Koss KSC75 are the equal of many full size cans and under $20. They will leak some sound, but closed and clip on for under $20 that sound better than a tin can isn't going to happen.
Earbuds: JVC-HAF130 "Gumy" series, under $10, and 95% or better of the SQ of last year's budget winner on Headfi, the Yuin PK2, which was $70.
In-ears: JVC-HAFX33 "Marshmallow" series, under $20, sometimes even under $10 on sale, and while very bass heavy (still much better than the low end Sonys), are good sounding for the money considering you'll have to spend at least triple their cost to see any improvement in in-ears.