Here's the verdict:
A few of the deleted scenes showed up in adverts(such as the Pizza Hut one) and books based on the first film.
Spielberg either has the footage locked in a vault somewhere or it was destroyed all the way back in '87 or '88 when they decided ultimately not to use it.
The idea that there's a tape or recording out there with the alleged Oasis scene is a dubious one, what I've been able to find is that it was probably cut early in the filming process, meaning it would not have been animated or voiced, if it even existed at all.
There here shots that were obviously cut and it can be scene in parts of the film(such as the Forging For Food scene).
What left is there to find? Its really all but speculation now.
Yeah, the oasis scene is the most obscure part of the cut scenes. Indeed, we don't even know if it was ever animated to begin with (maybe there are still some storyboards like the ones that had been posted online a while ago from the Sharptooth attack scene?) and for the other scenes.... well, we do know some snippets and most of what was supposed to be on screen. The only thing that's missing is really a full, uncut version of the movie. Not that it's likely to see that... but it's what we're still missing, right?
Somebody please tell me:
- why they made, drew, and colored scenes, and only after that they cut them, throwing hard work of animators into trash bin?
- why they had to close eyes on giant work of animators who brought these scenes to life, and DESTROY them, and not include them into behind scenes/extensions, where no scared small children who runs out of cinema hall, crying?
It's beyond my knowledge

As far as I know, the cut scenes were considered too scary for children and/or not significant enough so they were cut.
Another possibility is that they cut everything that was about racism (like the oasis scene, the scene where they found Spike or the scene where they're eating the food). All of them had possible racist themes:
1. Oasis scene: Speaks for itself, this scene was there to point out the stupidity of racism. The Gang soon proved that working together despite their differences in species got them food which leads us to:
2. Food scene: We know there's also a decent amount of footage that was cut from the film. In one of the trailers, Ducky is seen hugging Littlefoot and Spike before/while they eat. Who knows what else there might have been in this scene but maybe they talk about that oasis scene which is why it was cut as well. The cut is pretty obvious if you look at the scene by the way...
3. Scene when they find Spike: Well, we do know that Cera wasn't so happy about Spike coming along. This scene had potential for racist talk too so that's probably why it was cut.
That's my theory anyway (part of that has also been mentioned/theoreticised in previous discussion I do believe)
I'm completely calling for this as well, Snik. Such masterpieces of art that were made with so much love, passion and, of course, countless hours of work, simply mustn't be thrown away. Why they didn't include it as bonus material, only heaven knows...
