Sounds like you have inherited a very overgrown strawberry patch!
The dense growth can indeed encourage slug/snail/sowbug damage. However you may also have spotted wing drosophila flies.Was the damage mostly in the form of obvious nibbles, or did the strawberries just turn soft and mushy, with no obvious damage? If the latter, drosophila is likely. You won't know for sure until next season. However, just in case, a good cleanup (especially fallen fruit) and thinning will help reduce their population. If you think they are present, write again for help in dealing with them.
Strawberry beds generally benefit from re-planting every few years. If you don't want to go that far, a bed can be renovated by cutting back the old foliage, removing excess plants, and applying compost. At that time you can choose the healthiest plants or rooted runners, and keep those. It is a little late in the season, for that, but if you get it done right away they should still be OK.
You can make some guesses about what type of strawberries you have. If they bore lots of fruit in June/July, and then switched to making runners, they are June-bearers. If they have continued to make small quantities of fruit all season, with minimal runners, they are everbearers, or possibly day-neutral. Management of these types is somewhat different. You could have a mix of types, or all one type. Regardless, the June-bearers will take over the bed, and any other real estate they can reach.
Here is a good Extension publication on Growing Strawberries in Your Home Garden That will give you more details.