On this page of the game guide to Borderlands 2 you will find a detailed description of the side mission titled Claptrap's Birthday Bash!. You can start this quest in the Sanctuary location during the completion of the main mission named Bright Lights, Flying City.
2) Scooter's workshop
3) Moxxi's place
4) Marcus' shop
Accept the mission from Claptrap  and take the Invitations. Give them to Scooter , Moxxi  and Marcus . With the invitations distributed, return to Claptrap . Turn on the radio found on the shelf behind Claptrap and a timer will start. With over one minute in, take a slice of Pizza shown in the screenshot. Around 40 seconds till the end, Use Party Favor. Afterwards turn in the mission to Claptrap.