I got this adapter to go into the adapter that came with my headphones for my amp...but with distortion it sux with my headphones. And sound only comes out of my left ear.

Fender 25R Front man

Sennheiser HD202 Headphones

Radioshack converter
Eh, I use Vic Firth Sound Isolation headphones for musicians. I got them for about $50 at Guitar Center.
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You may need a stereo to mono adaptor, but most headphone jacks on amps are already wired correctly.
Its hard even with really good headphones to use high distortion and sound decent. Some amps (usually micros like Digitech or Zoom) have speaker emulated outputs. I use over the ear closed back wide frequency response expensive headphones, and I have to keep the distortion down.
headphones suck when driven by an amp... i dont know why... but i run my signal through a zoom 505 [just for reverb] and to headphones...
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same with me (with sound in one ear), also when i use them, sound still comes out of my amp.
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As uldhppi wrote, sounds like there's some kind of mono/stereo problem going on, since it's only the left ear which sound comes out of. I use a normal 1/8 to 1/4 inch stereo adapter sometimes with my Boss GT-Pro, and I know the same also works with my brothers Roland Cube. I was surprised your Sennheisers didn't come with an adapter, all of mine have... I'm not familiar with that particular model, though.

As for which headphones, it depends largely on what your budget is, but what you want to be looking for is something with high isolation and often also neutral sound reproduction. I sometimes use my Shure E4 IEMs, sometimes my Ultrasone HFI-780. I can easily recommend either of those, they are great. Absolutely no problems with distorted sounds.
Your amp sux. The signal it giving for headphone are too hot it makes them distorted.
You might need to buy an adapter some of sort to convert the signal somewhat friendlier for your headphone.
I've already dissed my amp long time ago. Using a POD which gives me 100% sound to headphone.