What is the difference between inte and ej and icke ?Feel free to just provide example sentences.

They all have the same meaning ("not"), but are used in different contexts.

"Inte" is the most common of them, and what is used in everyday speech.
"Jag åt inte frukost idag"
-> "I did not eat breakfast today"
"Jag vill inte göra mina läxor"
-> "I do not want to do my homework"

"Ej" is used in more official contexts, and often on signs of different kinds.
"Ej i trafik"
-> "Not in traffic", often seen on busses when they aren't in use or moving between two different routes.
"Parkering ej tillåten"
-> "Parking not allowed"

"Icke" is used very rarely in daily speech and writing, and when it is used it is mainly in a joking manner or to give a text an oldish feel.