How to know how many bitcoins does my offline generated address hold? Suppose I generate an address offline, using something like bitaddress.org

And then I receive some bitcoins on this address.

How do I know how much balance do I have on this address?
Whether an address was generated online or offline is irrelevant.

Any transaction that sends bitcoin to the address will be included in a block once it gets mined.

You can check the address balance by searching for that address in a block explorer such as https://blockexplorer.com/