The oblique stroke might also be called a skewed stroke. In DE shaving circles it is commonly called the Gillette slide. The Gillette slide is often thought of as a shaving technique for the advanced, more experienced shaver. However these days I don't believe one needs be particularly advanced or experienced to put the oblique-stroking technique to work.
First, the Gillette Slide with a DEThe frequent misunderstanding that seems to be causing the difficulty may be traced back to the early Gillette drawings that show the oblique stroke, the so-called Gillette slide, with the DE-razor edge parallel to the floor and the stroke direction being diagonal across the cheek. This has led generations of men to try to make a rather slicing stroke, which in fact is difficult to do. The difficulty comes from a backwards approach to the oblique stroke. By trying to emulate the Gillette drawing, with its diagonal, cross-cheek stroke direction and blade edge oriented parallel to the floor, this turns a simple technique into something more difficult and down-right dangerous.
The simple and safe mind set to using the oblique shaving stroke is to decide what direction you are going to stroke the razor. For example, in a first-pass stroke on the cheek, the with-grain stroke direction would commonly be vertical -- straight downward. Fine. So to make this stroke with oblique-stroking technique, instead of having your DE razor oriented with blade edge horizontal (that is, perpendicular to the vertical stroke direction and thereby parallel to the floor), angle the razor head slightly so that the edge orientation is off-perpendicular to the stroke direction. Then simply stroke downward!
It's all about how one conceives of the stroke. Instead of trying to stroke the razor so that the razor motion causes a slicing effect on the beard, it's much simpler (and safer) to make your usual stroke motion but with the razor's edge slightly askew. Ultimately either approach aims to get the same result, but trying to slice one's way to a Gillette slide may be hazardous to one's health. Simply turning the razor slightly and making a normal stroke in the usual directions is easy peasy.
Oblique Strokes with a StraightOld barbers' manuals on how to shave with a straight razor also advise using oblique strokes; this idea didn't likely originate with Gillette. I have run across this more than once in my leisurely perusal of such documents over the years.
Oblique strokes with a straight razor aren't difficult or dangerous either. Again, it's all about how you conceive of their execution. For example, when making with a straight razor the same with-grain, vertical stroke on the cheek (as discussed above in the context of using a DE), instead of stroking downward with the razor edge parallel to the floor, simply angle the razor slightly such that the heel of the blade leads in the stroke just a bit. It's really easy and very effective as well.
In other areas of the face and neck it may be simpler to orient the razor such that the toe of the blade leads in the stroke. In either case, the whole key to safe, effective oblique strokes lies in stroking the razor in the direction easiest and most appropriate. Simply fix the razor angle so it's slightly off perpendicular to to the stroke direction. Strangely enough, this is much more easily done than setting the blade perpendicular to the direction in which you would like to stroke, but then actually stroking on a diagonal to that desired stroke direction. Mechanically the desired outcome is the same, but more easily done with the recommended mind set.
Even with a new blade in my Parker SRX shavette, I have noticed a huge difference in the ease of safe stroking when I apply this oblique-stroke advice. The resistance to the blade is noticeably reduced when using oblique strokes, and especially with a straight razor, lower-resistance strokes mean safer strokes.