From the Universal York blog, this post on a whale displayed in a York County barn belonging to one Samuel Spangler sometime in the first half of the 1800s. The whale is described as having been caught in the Delaware River. This wouldn't be unheard of.
The Philadelphia Inquirer (December 6, 1994) reported that a 30-foot right whale (Eubalaena glacialis) dubbed "Waldo the Wrong-Way Right Whale" was found in the Delaware between Philadelphia and New Jersey. Wildlife officials managed to point it back towards the sea, but in early 1995 the whale had returned and was beached temporarily at an oil refinery near Pennsauken, New Jersey. "Waldo" was last seen in waters off Canada.
In April, 2005, NBC's Today carried reports on a beluga whale that had been seen around Trenton and Beverly, New Jersey. The animal was identified as one called Helis, whose native territory was in the St. Lawrence River. Helis had left the Delaware Bay around April 18, but by the 29th he was back in the river near Burlington Island. He was later seen near the Walt Whitman Bridge moving south. There were a few reports of the beluga from the Schuylkill River, but I don't know whether these were confirmed. By the end of the month, he had again moved out of the river.
The New York Times (May 1, 1922) reported that a 12-foot shark "said to have been of the man-eating variety" was killed by Joseph Fletcher in Tacony, Pennsylvania.
Several species of sharks live in the Delaware Bay and may make their way up the river; the Tacony shark is most likely to have been a bull shark. Other dangerous species such as the hammerhead and thresher exist in the Bay, but these prefer open waters and would not likely be found upstream. The bull shark is also the likely culprit in the attacks at Matawan, New Jersey in 1916.
The book Totally Bizarre Pennsylvania mentions a sighting of a supposed sea monster near the Benjamin Franklin Bridge in August, 1975. Peter Evangelidis reported that he and his girlfriend were along the river at Penn's Landing when he saw what he first thought to be a "bunch of black inner tubes or tires floating down the river, about 30 yards out" but that was moving against the current of the river. After a moment there was a violent splash and "this sleek head of an animal that should not have existed sprung its head out of the dark river no more than 30 feet from us". A canal cuts across Delaware, joining the Chesapeake Bay to the Delaware Bay. Evangelidis wondered whether the Chesapeake Bay sea serpent, Chessie, could have made it through the waterway and into Philadelphia. 1975 also saw reports of both sharks and whales from the Delaware, so it conceivably could have been one of these.
The above is the photo Evangelidis took of the creature.