You also say you only hear the US religious broadcasters and Radio Havana. Do you hear other stations also? Or are those stations you mentioned just the only *English language* broadcasts you hear?
I ask this because most of what I hear on the shortwave bands is foreign language broadcasts.
An example is the 49 meter band at night (5800 khz to around 6200 khz -- works best at night). I get a couple US domestic religious broadcasters in English, Radio Australia in English, Radio Havana in English, sometimes I get a Canadian station just over the border in English, and on some occasions I'll hear the BBC in English. But that's about it.
The rest of the stations are all in Spanish, Japanese, Vietnamese, Portuguese, Chinese, and Russian.
The 31 meter SW band (9400 to about 9900 khz -- also works best at night) is about the same here in the NW US. A very few broadcasters in English, the majority of them in other languages -- most of them from Asia and South America.
The only European SW broadcasters I have heard recently are Rumania in the 31 meter band and the Vatican station in the 31 meter band, sometime last year. Rumania was in English, the Vatican's program was in Italian. I also heard the Voice of Greece, it was in Greek. Back east (in your section of the US) there is probably more propagation to Europe, but you'll have a better chance hearing ham radio stations from Europe than SW broadcasters because there just aren't that many SW broadcasters in Europe anymore.
If you're not hearing many stations at all, my suggestion would be to relocate your antenna, or use a longer one, preferably outside. If you have a room in a second story you can use for DXing, put your radio and antenna up there, and see if that improves your reception.
And like KA3JJZ said, check the "DX / Local" switch on the side of the Radio Shack radio. If it's on "Local", it will cut the signal coming in from the antenna.
I don't know about the Grundig, but the Radio Shack World Receiver is a capable SW radio. Mine works fairly well on 25 ft. of speaker wire, as an indoor antenna. The broadcasts I mentioned above in my post are ones I've heard on that particular radio.
Also remember that sometimes the SW bands just don't work -- the ionosphere doesn't always refract the signals back to earth the same way. There were times during the middle of last year I would hear next to nothing on 25, 31 and 49 meters.