Taunt means to make fun someone or goad them to responding often in an aggressive manner.
"We should taunt the dog, its being laying lazily around."
Taut is when something is tight and under tension like on a bow or rope. It could also mean someone experiencing stress and anxiety.
"Your organ seems taut in those trousers."
Tout could be described as someone advertising goods, services and items to customers aggressively.
"Don't force me, you're not a tout."