What is the difference between intriguing and fascinating and interesting ?Feel free to just provide example sentences.

The difference is intuitive. They’re sometimes interchangeable, but at other times they’re not. You might say a mystery is intriguing/fascinating/interesting, but you wouldn’t exchange “I have an interesting relationship with my father” with “I have an intriguing relationship with my father”. Typically, if it is something that involves yourself or something you’re familiar with, you wouldn’t use intriguing/fascinating. Something about it feels slightly strange, or even egotistical. Mostly because they’re somewhat stronger adjectives than “interesting”. The other two are used when expressing an opinion, usually.
Another difference is that you can say something is slightly intriguing/interesting, because it’s not that cool or important, but you can’t say something is “slightly fascinating”. “Fascinating” is something that really catches your attention and holds it completely. A smile from a stranger may be intriguing, and an unusually-patterned tile floor may be interesting, but an unsolvable crime is fascinating.