Can I offer the prayer in the clothes I sleep in (pajamas)?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

It is permissible to offer the prayer in the clothes you mentioned as long as they are pure, cover the body and are not transparent. Otherwise, it is not permissible because covering the ‘Awrah as well as being pure of Hadath and Najas (impurities) are two conditions for the validity of the prayer.