Elliptical craters can be studied three ways: Laboratory simulations, computer simulations, and observations.
Laboratory simulations have not really been done in detail for this problem in decades (I don't know why, I'm not an experimentalist). The most recent big modeling study that I know about is Collins et al. (2011) and Eibeshausen et al. (2013). The former tried to determine what fraction of craters should be elliptical on different solar system bodies, while the latter looked more at that impact angle dependence as a function of other model parameters like pressure. I suggest going to the Eibenhausen et al. link which is open-access and Fig. 5 shows ellipticity versus impact angle (yes, there is a continuum to answer your question) for a few different pressure regimes.
Observationally, this is rarely studied when building impact crater databases. Primarily, the reason is that it's of less interest and it requires more effort. Usually, people will just try to find craters that look elliptical and then, effectively, eyeball the axes and record the major and minor axes lengths. The problem with this approach is that one must visually recognize the crater is elliptical and then one must subjectively choose those axes. This then could be compared with a "background" crater population if one has also measured craters that are more circular. An example of this work would be by Bottke et al. (2000).
A better way to do this (in my opinion) is how I have attempted to study this question. It begins by tracing the crater rim and then fitting an ellipse to that trace as well as a circle, and doing this for all craters. I did this with my Mars crater database (Robbins & Hynek, 2012), though the ellipse analysis is in that Collins et al. (2011) paper. In doing this, there are some problems, though. One is that any bias in how the rims are traced is going to bias the ellipse results, which are much more sensitive to inaccurate rim traces than circle fits because there are more free parameters. Another problem is exactly what technique is used to fit an ellipse. There are lots of different algorithms out there, and many that are the most popular are severely biased in various ways.
I tried to quantify both of those effects in my lunar crater database (Robbins, 2019) by doing a lot of different analyses and playing with a lot of different ellipse fit algorithms. The supplemental material that discusses most of that is not behind a paywall. After all those things are factored in, the conclusion is that more craters are "elliptical" than are predicted by simulations, but here again there's a problem: What is "elliptical?" Is it when the major axis is 10% larger than the minor? 20%? 50%? 100%? This gets to that problem I mentioned with the Bottke et al. (and similar) studies – when is something visually elliptical enough to count it as "elliptical?"
That said, there is also a problem of studying elliptical craters in the question of: Did the craters form that way? Differential erosion could cause craters to erode more in one direction and thus become more elliptical as they degrade, especially if they are on slopes. Another problem is that secondary craters – craters that form from the ejecta of larger, primary craters – form at lower velocities / energy and so are almost always more elongated, so removing those from a primary crater population before studying their ellipticity would also be desired. This gets to be a problem on the Moon where we might have lots of unrecognized, multi-tens-of-kilometers secondaries from basins that affect what would otherwise be interpreted as primary elliptical craters.
I suppose if I had to summarize all of this, it would be that elliptical craters are, indeed, studied in and of themselves, but there are relatively few of those studies, in part because there is not necessarily too much new science there (is it worth spending a year on a computer to slightly refine percentages? or $millions in a vertical gun lab to refine things slightly?), and in part because the observational study of them is quite difficult due to the time-consuming nature of gathering the data and then understanding the biases in those data before any analysis can be done.
