Best for the "what is this" reaction.
For peak strange-by-effect impact:
Jackson Pollock — move the cursor, splatter paint in real Pollock palette. Has been quietly online for two decades; still hypnotic.
InspiroBot — AI-generated motivational posters. Click to generate. The outputs range from accidentally profound to actively threatening. The bot has its own dedicated subreddit; the best outputs end up in art galleries.
Ever Dream This Man — a 2010 internet mystery. The site documents a face that thousands of strangers worldwide claim to have seen in dreams. The "investigation" framing is sober. The premise is uncategorizably strange. Subsequently revealed to be a viral marketing project, but the site remains as documentation.
ZomboCom — a single Flash animation (now HTML5), launched in 1999. A spinning pinwheel and a deep voice intoning "the infinite is possible at Zombocom." Has been continuously online for over 25 years. The voice still sounds the same.
MapCrunch — drops you at a random Google Street View location anywhere on Earth. Click "Go" and you're somewhere. Could be a Mongolian highway, an Argentine suburb, a Norwegian fjord. The lack of context is the experience.
These five reliably deliver the strange-by-effect register inside thirty seconds.