the oval on the sidewall of a tire tells you the "born on" date. The first 2 numbers are the week, the second 2 are the year.
For example in the below oval, it's the 8th week of 2014. So this tire is ready to go to preschool...
If you don't see an oval, look on the other sidewall. It's also possible for really old tires to not be marked (but those would have to be... ancient).
As tires sit, whether on the bike or off, the heat cycles from cooling down at night and warming up during the day will make the oils in them evaporate and turn them wooden. Even in a warehouse unmounted, they'll still age. You can see when online retailers drop prices radically on them, usually they'll be slightly older tires and there's a very good reason for that: it's because the generally accepted guidelines for tire age are
- Sportbike: no more than 2 years old
- Sport Tourer: no more than 3 years old
- Cruiser/Dresser/Tourer: no more than 4 years old