Could be a bad impression of a Geordie accent, from Newcastle in NE of England.
It took a moment before I realized you must have meant “coin” and not “corn” because my mind went off in a direction I don’t advise. 
I think you need to divide this question into two parts–
- warsh for wash. As most have replied, this is usually associated with rural people in the US, and I’ll almost bet that it would go back 100-200 years and be almost exclusively from the rural South. Living in Virginia and Ohio the last 50 years, it’s mostly associated with rural people from Kentucky/W. Va. and a few other locations. I have no doubt that many of the people who have offered that their relatives living in parts of Illinois/Indiana, etc had their origins in more Southern states.
2… terlet. This one is more complicated. It certainly was a pronunciation used by many older people in the NYC/NJ area. It was also used somewhat in Black English in the old days. You can link it to the same thing that caused the older generations to say boid for bird. If you go back to the Bowery Boys movies of the 1930s-40s, you can see some of them saying things like boid and thoity-thoid for 33rd.
It may well indeed have migrated with many people from parts of England and been used in the US wherever they settled. But, as people went to schools, that kind of accent would probably have been conditioned out of them.
I have an idear, let’s flush the terlet: NY and spread out to NE USA, especially major urban areas, but NY still owns it.
Wersh or warsh: Seemingly rural everywhere.
Usage has spread, obviously.
Another vote for Brooklyn
I grew up in Archie Bunker’s neighborhood, and it wasn’t unusual to hear blue collar guys in Queens saying “flush the terlit.”
But it was more common to hear Brooklynites reverse the “er” and “oi” sounds. Hence, “bird” became “boyd” and “girl” became “goyl.”
That’s ALSO common among old-timers in New Orleans. That’s is why John Fogerty tried to so hard to saying “boyning” and “toyning” in the song “Proud Mary.” He was a California boy trying to sound like he was from New Orleans (which actuallymade him sound a bit Brooklynese.)
No! No! No! You’ve made me think of Leonard Nimoy’s version of that!
I’m seeing a lot of "rural accent’ in here, but what exactly is that? There’s different accents spoken in rural areas throughout the United States; a farmer in Iowa probably isn’t going to speak in an Appalachian cackle.
I came in to say “Queens,” specifically because of Archie Bunker.
I’ve heard a fair amount of Brooklynese spoken from the 1970’s onwards. In my experience, neither “warsh” nor “terlet” are common at all. In fact, I remember both Archie Bunker’s and Ed Norton’s pronunciations because they sounded so strange to me. Perhaps this is an older way of speaking.
Typically I hear:
this -> dis
idea -> idear
three dollars -> tree dolluhs
Both my Mother’s parents and my Father’s parents emigrated from Germany just before World War I; both sets moved directly to and lived in Southern Illinois their entire lives, settling about 150 miles away from each another. (Waverly and Marion). All my grandparents say “warsh.”
“Idear” is typical of certain Boston accents.
Same here, and I hear it every day at the carwash I operate in the West side of Cincinnati.
Its also almost always associated with older people buying the cheapest wash option, as in “Just give me the regular warsh” or “Just a basic warsh”.
Older people in Western PA say warsh, but younger people are as likely to pronounce wash as woosh as wawsh.
Never heard terlet except from people on TV.
Belfast, Ulster, Northern Ireland maybe?
Noooo… it’s definitely not British! Especially not Surrey. It’s not west country, northeast or Northern Irish either. It’s American.
This reminds me of Billy Bob Thorton’s accent in “Sling Blade”
“Poor little feller”; “I’d like some of them french fried pertaters…”
Thinking about this a bit more. I’d second the idea of an English West Country accent:
http://www.youtube.com/watch?v=THCht3I7yeI
My Geordie idea worked for ‘terlet’ but wash would would be more like “w-ash” (ash as in ashes).
It’s definitely not British, there’s no British accent that would use the ‘terlet’ pronunciation. I’ve been trying to think of how to write down how it would be pronounced in the West County or by Geordies, but I’m struggling a bit. It wouldn’t be ‘terlet’ though. Any British accent I can think of would pronounce the ‘o’.
Sounds Baltimorese to me.