We have noticed our clothes smell after they are washed (washing machine is 3 yrs old). Both the dishwasher and washing machine also have an odor after they cycle through. We had a plumber tell us he thinks the issue is corrosion in the hot water heater (7 years old) fouling the hot water. Is that a possibility?

Yes its possible but not probable. Try washing your clothes on cold only. Is there still a smell. Water heaters can also build up bacteria which can make a sulphur like smell. Is that your smell