1. Fruits, such as, apples, oranges(,) and grapes, are tasty
2. Fruits, such as apples, oranges(,) and grapes, are tasty
3. Fruits such as apples, oranges(,) and grapes are tasty
I couldn't find an authoritative source, but here are my thoughts:
By convention ".e.g." is preferably followed by a comma in AE. That is the only possible (but unconvincing) argument I can see for the comma following "as" in Version 1. Otherwise, I would say there is no sensible reason for that comma. You wouldn't dream of writing "similar, to apples" or "like, apples", so why write "such as, apples". So I, personally would say: Version 1 is wrong.
IMO versions 2 and 3 are correct but different in meaning:
When enclosed in commas the phrase "such as apples, oranges(,) and grapes " is parenthetical or non-restrictive. It implies that all fruits are tasty and that apples, oranges, and grapes are examples of fruits. Since everybody thinks they know what a fruit is, without the need for examples, Version 2 -- though correct -- represents an unlikely meaning.
Without commas the phrase in question is restrictive: only fruits like apples, oranges, and grapes are tasty; fruits like tomatoes, aubergines and peppers might not be tasty.
So Version 3 seems the only sensible version to me.