Greek yogurt is made from milk; therefore, it does spoil. Unopened Greek yogurt or strained yogurt can last two to three weeks beyond the sell by date, assuming it is stored properly at the correct temperature. You should never leave Greek yogurt at room temperature for more time than is necessary because it will spoil quickly.
Any discoloring or mold on Greek yogurt means it is no longer good. Additionally, if the smell seems off, it is best to discard the product. Greek yogurt typically should not smell overly sour or have a yeast smell. A murky, watery layer on the top is natural and can either be stirred back in or dumped off. That watery substance is just the whey that has settled to the top and it actually has nutrients like calcium and probiotics.
You can freeze Greek yogurt for up to two to three months. It is best to freeze it when it has not already been opened to preserve the freshness. Once the product thaws, take a small bite or smell it to check if the yogurt is still good. Greek yogurt may not maintain its original texture after frozen and then thawed. It is to freeze a small amount of Greek yogurt, thaw it, and then determine if you like the texture before buying a cart full.
To sum it up, Greek yogurt does spoil, but it will typically last a couple weeks or more beyond the sell by date. You can freeze Greek yogurt, but the texture may change upon being thawed. Do not eat Greek yogurt that has mold or is a different color from the original color. Any strong yeast or sour smell means it is probably bad. When in doubt, just trash it. While Greek yogurt can be exspensive, it is better to be conservative about spoilage than risk being seriously ill.