What might be causing the sudden onset of pain and stiffness in the joints of my fingers ?

Systemic Process: If we are talking multiple fingers on each hand, it will likely be a systemic process. Meaning a pathology which is affecting your whole body. Such as systemic lupus, rheumatoic or psoriatic arthritis, reiter's syndrome. Psoriatic arthritis likes to affect the small joints. If otherwise than common everyday arthritis certainly, can cause "stiffness" but is usally not with "sudden onset.".