when i think of ASX European stock options two words immediately come to mind - horrible liquidity. followed by two more words - hideous spreads
you can tell European options by the strikes, they are usually one cent higher than the strikes of the American ones. your brokerage platform should indicate this as well. i don't have a list of which stocks have them, but it would be only the very largest caps, maybe only the top 10
i experimented with these some time ago as part of my naked put --> dividend strip --> covered call strategy. the idea was to write near ATM naked puts expiring the month before ex-div date, take delivery if assigned, then turn around and sell 2 month covered calls over it
since i didn't want to get the stock called away, at least not until after it had gone ex-div, i tried using European options on the covered calls. and quickly gave up on the idea after a few months. the liquidity is terrible, the spreads are ridiculously wide and i often didn't even get a fill going 3 or 4 ticks to their side of the mid
so i went back to using the American options. more of a hassle having to watch it more closely just before ex-div in order to be ready to close out if necessary to protect the stock position from being called away, but way better fills
of course these days i don't use the strategy very much anymore due to no margin on IB