How large is your suitcase? Amtrak's carry-on rules, historically speaking, are loosely enforced compared to the airlines. They announced a stricter policy as of October 1, 2015, but it is still quite generous— two bags weighing up to 50 pounds (22.7 kg) each plus two personal items weighing up to 25 pounds (11.3kg) each for free, then $20 for additional items or items above the quantity and size limits.
On Amtrak, "no checked luggage" means that you cannot check your bags with Amtrak (e.g. if the train has no baggage car); you can still bring them onboard and look after them yourself. Some long-distance trains that run on parts of the Northeast Corridor (e.g. the Cardinal, Silver Service, the Vermonter) do have baggage cars, but all will have overhead racks as well as shelves at the end of each car where you can stash your bags.
As of 2015 there are no intercity buses to Philadelphia which depart directly from EWR (Trans Bridge Lines only serves some Northeast and Central Pennsylvania destinations). You would need get to Newark Penn Station, where BoltBus and Greyhound connections are available, or backtrack to New York City. BoltBus and Greyhound will both have luggage compartments. This will, however, require a commuter train or bus connection, vehicles which will not have luggage racks or storage. The $30 or so for a taxi may be worth it, but note that you would be arriving after the start of rush hour.
Note also that the Greyhound station in Philadelphia is located near the Market East Station, not 30th Street Station. To get to UPenn you'd need to take the Market-Frankford Line from 11th Street. BoltBus and Megabus stop at JFK and 30th Street near 30th Street Station, which is a longish walk to Penn; with a large bag at night, a taxi may be a better idea. You will arrive in Philadelphia too late for the LUCY shuttle.
Directly from the EWR train station you could take an NJ TRANSIT Northeast Corridor Line train to Trenton, then connect to a SEPTA Trenton Line train to Center City/30th Street (you should now be able to purchase the transfer ticket directly from NJ Transit). Allow 5-10 minutes to transfer at the Trenton Transit Center. There is a penalty for on-board ticket sales, but you can receive credit for the difference if you are making a round trip.