How to American and European options differ from Asian options?

Answer 1

The difference does not lie in the strike price, it is on the date on which you can exercise them:
-European Options can only be exercised on the expiration date
-American Options can be exercised at any time between the acquisition and the expiration date
-Asian Options can be exercised at the expiration date or at previously established dates, for example on every last trading date of each month between the acquisition and the
expiration date

Answer 2

I am assuming you are talking about the settlement style of the options and not where the options are traded.

American and European style options both have fixed exercise prices, call the strike price. American style options can be exercised any time prior to expiration, while European style options can only be exercised at expiration.

An Asian-style option has an exercise price equal to the average price of the underlying asset over a given period. An example of an Asian-style option is the NYMEX Heating Oil Average Price Options

http://www.nymex.com/AT_spec.aspx