I have this problems sometimes with my tea kettle. Though I've never washed my first with soap, I always brew a pot of vinegar (even apple cider vinegar) to get smells and stains out. Maybe try to boil a pot of vinegar, then pour it into your carafe and let it set for a few minutes. Then just rinse it out with water.

Again, haven't had the same issue, but it's a cheap try. Good luck! Soap flavor coffee doesn't sound too good.

I currently have this issue with a Thermos I love (1litre). Anything hot that goes into it comes out flavored with Dawn...or whatever I was using at the time. I've traced it to the rubber o-ring and plastic cap. I used extremely hot water to wash and had the cap sitting in the soapy water for longer than I was expecting.
Plastic notoriously keeps the flavors of whatever hot it holds (why I like steel or aluminum), so you need to get rid of all the plastic or get a new carafe.
Next time you clean something like that try using vinegar. I use an electric tea kettle to heat the vinegar and scrub with a clean brush, then immediately rinse. Gets most of the grit and grime out without odd flavors.

I would mix some baking soda and some hot water and let it set in your carafe. That might remove the nasty soapy smell & taste. In the future, get your self a jar of Brew Rite coffee pot cleaner. (I got mine for under $5 at Wegmans.) It's the best at cleaning out old coffee remains from coffee pots, carafes and travel mugs. I use it all the time on my thermal carafe coffee maker and my espresso machine.

Lemon juice. The acidity works as well as vinegar, but will leave an unnoticeable aftertaste.

Maybe try some denture cleaner (Efferdent or similar)? That's what we clean our carafes with around here, and they come out sparkling, but there's never any aftertaste.

Fill it with a solution of 50% distilled water and 50% white vinegar. Allow the solution to sit in the carafe for about 15 minutes. Pour out the vinegar/water solution, give it a good rinse and repeat as necessary. Vegetable based soaps, such as Mrs. Meyer's, tend to leave a residue than their "better living through chemistry" alternatives.

I have a question: What is distilled water and why would or wouldn't I use it in place of regular water?

"Distilled water is water that has many of its impurities removed through distillation. Distillation involves boiling the water and then condensing the steam into a clean container."

You use distilled water when you need water that is free of impurities that can otherwise leave behind mineral deposits (and such as mess up a science experiment, or the brewing of a beer, or in a steam iron so there won't be things deposited on the cleanly pressed clothes).

Thanks, caseoftornados! I couldn't have said it any better (re: distilled water).

Yes, thank you!

Question: can you drink it?

Mrs. Meyers tends to leave soapy residuals for us, too. I have learned that only a teen bit of soap is necessary. I would also try the vinegar or baking soda.

http://thesweetest3.com/

@leepert: Yes, you can drink distilled water. It's nothing more than purified water.

If all else fails (that vinegar should do the trick), go to a homebrew supply website, and get some PBW. That stuff will take anything out of anything, and is non toxic. It was invented to clean nastiness out of any type of container, tubing, glass etc that you can find in a brewery. My wife's tea thermos gets real nasty, and it worked better than vinegar.

Also, with PBW, a little goes a looooong way.

I'd try baking soda. Let it soak up the flavors. At least you use Meyers!

Lemon juice works wonders and it's a cheap solution.

I've always used hot water and kosher salt (plenty of it) to clean coffee carafes. Picked that up in a restaurant I used to work in and it works well.