I don't have the program and the site documentation is sparse. They also have a pay version of the program (about which I also know nothing), that may have documentation.
If the program can do slices in arbitrary planes, that would be the simplest.
Can the program do intersections of objects? For instance have the oval tube pass thru a wall (flat plane) then inspect the shape of the result. Perhaps the tube should be a solid for this approach so the area on the plane can be subtracted, thereby showing a hole of the desired shape.
Here is a real 'out-of-the-box' idea: If you have a projector, slide or video, project the oval on a screen then rotate the screen to the desired angle.
The projection problem seems similar to projecting a shape on a display. If you assume the display is a CRT it's a little easier to think about projecting onto the screen face. This is a solved problem in computer graphics that is used in 3-D design programs. You would angle the tube as needed then move the observer viewpoint to the inside of the tube.
There is probably a straight-forward mathematical approach to the problem. Perhaps one of the math wizards on the site can come up with one.
Cheers,
Tom