Hard to believe, but yes UA did take delivery of A319s, 777s and a 763 after 9/11

According to http://www.planespotters.net/Airline/United-Airlines the youngest aircraft in the UA fleet is N855UA, an A319 that entered service in May 2002. N229UA is the newest 777, and it entered in March of 2002.

The oldest in the fleet is N318UA, a 733 that is 21.2 years old