What do “virgin” and “extra virgin” mean in regards to olive oil

I don't want to disappoint you, but the sad truth is that extra virgin olive oil is unsuitable for all the cooking methods you mention. When you heat any oil past its smoking point it starts to deteriorate and can even become dangerous. Olive oil, extra virgin in particular, has a lower smoking point than most other oils. In fact, you will be better off with an olive oil of lesser quality. Such an oil will have been processed and thus purified, increasing its smoking point.

You may think that butter is unhealthy, but at high temperatures it will actually withstand the heat better than extra virgin olive oil.

Good oils for the purposes you mention are canola oil, sunflower oil, peanut oil, and grapeseed oil.

See What oil or fat to use for different purposes? for a general discussion about choosing oils.

If you are using unrefined avocado oil, you it will have a unique flavor that will affect your dish or outcome, and in that case, the flavor would be the primary purpose.

If you are using refined avocado oil, its main unique characteristic is that it has an unusually high smoke point at about 480 F (250 C). While this may make it exceptionally suitable for applications like deep frying, you would have to consider whether the cost is justified, given that many more available and lower cost oils (at least in much of the world) perform very well, and most deep frying temperatures don't exceed 375 F (190 C).

As to a drawback—if you exclude cost—no, there is no reason to avoid refined avocado oil in recipes.