I did some research and here's are some different people's experiences:
Yvonne Garcia on http://www.petfish.net/articles/Cichlids/oscar.php
said, "Plants: Oscars are ground diggers, plants don't stand a chance with them.......WRONG! Plants and Oscars can successfully be kept together in a tank. When choosing plants for any cichlid tank, it's a good idea to follow a few rules (not rules, but good ideas): Stick with plants that taste badly to fish, stick with plants that can be tied to rocks/driftwood, and/or stick with plants that are bulbed and can be buried deep within the substrate. Some plants to consider: Bolbitis heudelotti, Cryptocroyne balansae, Crinum thaianum, and Anubias."
Katt, altaaffe, and John L. on http://www.theoscarspot.com/viewtopic.php?f=62&t=15788
said, "Plants for Your Oscar Tank.
Yes, believe it or not, some Oscar`s will leave live plants alone. Unfortunately most Oscars won`t. For those of us, who have the second kind, planting an Oscar tank will be mostly trial and error.
There are a few thing`s you can try to help give the plants a fighting chance.
Use plants that grow on wood and rocks. Or place them in the middle of the tank so your Oscar can swim along the front or back of the tank. Leave place`s in between, like hallways.
If your Oscar pulls up the plants try re-planting them in a different location. You don't want your chair in front of your door, well it might be your Oscar doesn't want that plant in his way either.
using rocks at the base of the plants, might or might not help.
Oscars like low light, so go with plants that grow in low light conditions. That way you wont need to upgrade your lighting.
Here is a list of some plants you can try.
Will grow on wood and rocks
Java Moss (Vesicularia dubyana)
Java Fern (Microsorum pteropus)
Windelov´s Fern (Microsorum pteropus 'Windelov').
Plant in gravel or sand
Green Wendtii Crypt (Cryptocoryne wendtii 'green')
Brown Wendtii Crypt (Cryptocoryne wendtii)
Elodea (Egeria Densa) Can also be floating. Could use a little more light, but can live and reproduce in low light conditions.
Water Sprite (Ceratopteris thalictroides) Can also be floating
Temple plant, Starhorn or Giant Hygro (Hygrophila Corymbosa)
Aponogeton Crispus plec eats sometimes
Stargrass (Eicchornia Azuria) this is a tall stem plant that as it reaches the surface changes leaf type to become more of a floating plant
Floating plant`s you can use. They can get in the way of feeding, and will need to be thinned out often.
Duckweed (Lemna sp.)
Water Lettuce (Pistia stratiotes) gets big.
Eared Watermoss (Salvinia auriculata)
Theses are some of the plants that have worked for me. So give it a try you might be surprised.
One last word on buying plant`s. make sure they come with a care tag, or you just might get a bog or house plant, that will rot in a month or two and cause water problems.
For those with plecs be aware that a large number of them will see the broadleaf plants as food & it's not always the O that is destroying the plants."
Myself, I've never kept an oscar. I have, however, kept the plant Ceratophyllum demersum, AKA hornwort or coontail. It's a very spiky plant and I could imagine a plant-eating fish would be unable to eat it. If you grab it, it's so hard and sharp that it kind of hurts your hand. So maybe that might work, too, on top of all of the plants listed above. Good luck with your fish :)