Why we offer butter and betel leaves garland to Lord Hanuman?

Betel Leaves: 

After the success in the war against Ravana, Sita Devi spotted hanuman in a betel leaf garden when hanuman bowed to her feet seeking her blessings. Sita devi plucked few betel leaves and showered on hanuman in order to bless him, so the tradition is still followed. 

Another story goes that when Sri Hanuman conveyed the message from Sri Rama, Sita Devi garlanded Sri Hanuman with a betel vine as a token of Her joy and appreciation, as she could not find any flowers nearby. 

Betel leaves should be made into a garland with a piece of arecanut in each leaf. 

Butter: 

It was during the Rama Ravana war. Ravana was trying his best to defeat Rama. But each of his weapon was squashed by Rama's arrows. Rama was being carried by Hanuman as at that time. He did not have a war chariot like Ravana, whose ratha was magnificent. 

Ravana was becoming frustrated. Ravana changed his tactics. Instead of attacking Rama he started to shoot at Hanuman who was carrying Rama. Hanuman had got the boon of immortality from Brahma but that did not prevent him from getting injured. 

Lord Rama began to fight like a whirlwhind and soon made Ravana run from the battle field. Our Lord tolerates any amount of hardship but cannot see His bhaktas being troubled. When they retired to their camp Rama made Hanuman to lie down and inspite of his protests called for cool butter applied it Himself on Hanuman's burning wounds. So, the tradition is still followed.

Jai Sri Ram