The house we rent was buildt in the 80's. When it rains we get a foul smell from master bedroom. We have checked for rodents in rain gutters and took room apart to look around. Smell has gone on for a year. Our toilets get plugged very easily. We had one toilet replaced. Our entire house looses water pressure from time to time. We have some soft spots in our lawn. Someone looked under the cover on sidewalk and saw our water main valve and meter is under water. The sprinkler main is also under water. What does this mean? Is something backed up? What can I suggest to the landlord? We are thinking about moving because we are tired of these problems.

If you are moving, don't concern yourself over it.
As for water on the meter, does the meter turn when no one is using water? If so, you have a leak, if not, the water is either on the city side of the meter or is ground water.

If you live in an area that is subject to low temperatures, ice developing around the valve can't be very good. Maybe your line could freeze shutting off your supply and/or causing damage to the valve and meter and more leaks and more water.

The meter under water isn't a good thing. The landlord should have the water company check it out. It's probably a break and it might be the landord's responsibility to fix it.
The leak could very well be the cause of the low pressure.

Rain could cause sewer overload, where sewer water essentially backs up from the street into the house's sewer system because of a break causing the smell.

Trees near the sewer line make sewer breaks a distinct possibility.