I paid off $2500 worth of debt a few weeks ago and I got my score today and it's still showing that debt I owe thus my score hasn't changed (in fact, it dropped a point 
)
It depends on the credit card. Here is what mine did this last cycle:
US Airway's statement closed on April 4th, and it updated on April 8th to EQ and TU.
Wells Fargo CC statement closed on March 22 and updated to TU on March 28th but has not updated to EQ yet.
Capital One statement closed on March 10th and updated by the 14th on EQ and TU.
Starting Score: 583 EQ, 612 EX, 569 TU