Alternatively the washer drain standpipe is too skinny or is not built to code, or the drain system is not adequately vented (mouse or bird nest inside up above?). The current code calls for a drain standpipe and trap at least 2 inches in diameter. I'm not sure how much horizontal distance from the trap to the main drain is allowed.
The washing machine drain may be old enough to be grandfathered but some modern washing machines can pump out water faster than an older drain can handle.
Tornado victims: Do not rush to rebuild. Take your time and look for and get a good contractor. Or consider selling the property and moving to a home that is ready to live in.