Just some impressions off the top of my head: 'Twirl' is usually a transitive verb. If a person twirls an object, they're moving it round in a light, repeated circular motion. Think of a cheerleader twirling her baton. NB The initial 'tw' of the verb often indicates a light movement with a person's fingers - think of tweak and twiddle. Also words like twist and twine. 'Swirl' is often used for liquids - think of eddy in a stream, or swirling cream into your coffee. It's also used in graphics to describe a loose, fluid curling shape. Try googling some images for 'swirl' and you'll see. 'Whirl' is similar, but it's usually faster, with more repetitions. Unlike swirl, whirling suggests complete revolutions, repeated many times. Think of whirling Dervishes. Whirling round can make you dizzy.