Might be the hamper .

How do you dry your clothes? Are you able to dry them outside in the sun?

It can happen if you leave your clothes in the washer overnight instead of putting them straight into the dryer when they are done.
My washer and dryer sit in a room that is not very well ventilated nor lit. I keep the washer door open when it's not in use and I put freshly washed clothes straight into the dryer once they are done. Once a month, I toss a couple towels in the washer soaked in bleach and let it run on the hottest water cycle and the longest wash/rinse cycle. (I have front loaders). That seems to keep the smell at bay for a while.

Vinegar kills mold and mildew and does not damage anything if you spill it so you can use it all over the house....I sprayed some boots I took from the basement...killed the mold''also sprayed sidewalk that had fungus.; and the smell goes away.......I buy borax for the floors freshens and does in tiny bugs like fleas and ants

Leave the door to the washer open when not in use. The air circulation will prevent mold from growing behind the tub lining. To rid any mold you may have now, fill the washer with hot water, then add several more gallons of hot water manually. The water needs to be above the fill line. Add 2 cups of bleach and let drain. Turn washer off. Don't fill for the rinse cycle for about an hour, then turn washer back on and let it rinse and finish the cycle. Do not wash colored clothes right after a bleach wash, drops of bleach water stay behind the tub and will put brown spots on colored clothes.

here in Fla. you have to hang or dry clothes within an hour or two, unless they have bleach in them.
If I get a 'stinky' load, from forgetting, I have to rewash 2-3 times with soap and vinegar. I use about 1/4 - 1/3 of a gallon jug, when that happens to me.

don't let damp clothes sit in the hamper.

this is definitely a dampness problem. where there is regular dampness, like florida or new jersey, there is mildew or mold. you cab sprinkle cornstarcth or any other absorbent stuff. try those little packets of granular beads that the put in shoes, in your hamper.

the main thing is to get the clothes out of there as soon as possible. i had that problem and the only thing i could do was run a dehumidifier day and night. uh uh! now i open a teeny little window and leave it open (only a monkey can sneak in) not in the winter - and when do a wash, i run a fan. i find that in the winter when the heat is one, it's much better. is that true with you, too? that's because the dampness is less and so is the mold and mildew.

you can see from the answers that it's a common problem with closed-in washers and dryers. quiltncrazy and i are supporting the vinegar industry.

My daughter's washer was the same way and I replaced the hoses to the machine and the problem went away...

I have to add vinegar to every load, I thought it was becasue of having well water. even though it doesn't smell to drink and taste good. my towels and sometimes other clothes will come out smelly. even with fabric softner. but the vinegar does the trick.

Our carpet mildewed when someone got a little aggressive with spray part of the carpet cleaner and didn't suck up all the water. We did this just before a vacation and came home to a smelly carpet. I called the county extension office and they recommended trying ammonia, worked wonders.
So now I put ammonia in the towel load of the washer and will add it to any sour smelling clothes, have not had it ruin any fabrics, but haven't really done it on any delicates.

We had this a couple of years ago and found out our washer was not dumping all the water...since you have a new one I'd say to check your pipes that drain....could be a missing sock:)You can verify if this is going on by using your hip and push the machine back in a tilt when clothes are out...if you hear a slosh...it is water in there! If all is well....and you are drying as soon as they are done washing....then try the vinegar and/or a fabric softner....remember,this is the fall and here in the country we know that our ponds and such 'roll over'....this could be a seasonal thing for you:)Skeat