What is an 18K gold vintage man's Olma wrist watch worth?

if in very good condition and a standard movement , its likely a $300-$500 USD piece.

if its a chronograph or chronometer they are quite a bit more in the $900 - $1500 range depending on model.

If watch is running but rough condition its a toss up if the scrap value of the gold is worth more then the watch or not.

If its not running and needs anything more then light service to repair then scrap value would likely be higher .