Das, was and welches (or the equivalent masculine and feminine versions) are basically no more and no less interchangeable in German than that, what and which are in English. I think the real problems with your translation are elsewhere. As a native speaker I can't even get an intuition about the proper choice of relative pronoun before we have fixed the main clause.
»X«, »Y« und »z« sind alle Beispiele für ein Oxymoron.
Languages differ in how to deal with certain breaks between singular and plural. E.g., "Menschen schauen auf ihre Armbanduhr, wenn sie ungeduldig sind" translates to "People look at their watches when they are impatient" and vice versa. If you use the plural in German, it means that each has several watches. If you use the singular in English, it means that the people all share a single watch.
With Beispiel für/example of it works the other way round. We have two options.
‘X’, ‘Y’ and ‘Z’ are all examples of an oxymoron.
»X«, »Y« und »z« sind alle Beispiele für Oxymora.
As you can see, if you put Beispiel into the plural, you must do the same to Oxymoron. This rule isn't really logical at all, but that's how it works. (I think English accepts the illogical variant as well, but German is more picky and actually insists on it.)
‘X’, ‘Y’ and ‘Z’ are each an example of an oxymoron.
»X«, »Y« und »z« sind jedes ein Beispiel für ein Oxymoron.
This construction is identical and correct in both languages, but I think it is not used as often in German as in English. The reason is that if the things enumerated don't happen to have all the same gender, there is no logical way to choose the gender of jeder/jede/jedes. Therefore, we are so used to substituting the illogical alle ("Sind alle ein Beispiel") that even when it isn't necessary, not doing the substitution feels just as wrong as doing it.
Perhaps due in part to the practice of substituting alle for jeder/jede/jedes, but no doubt also to prevent the restrictive reading of alle (meaning it's a complete list - a distinction that English does here through all vs. all the), it is also common practice in this kind of sentence to substitute alles for the actual, more logical alle:
... sind alles Beispiele ...
... sind alle ein Beispiel ...
All of this is relevant because the choice of relative pronoun (or at least of its form) depends critically on whether it refers to a singular (Oxymoron) or plural (Oxymora). So this is your first main clause corrected:
»X«, »Y« und »z« sind alles Beispiele für Oxymora.
And now the problem is that we can't refer to the plural of a term in a relative clause defining the singular -- in German no more than in English. This only leaves us with the slightly problematic colloquial option if we want to avoid restructuring:
»X«, »Y« und »z« sind alle/jedes ein Beispiel für ein Oxymoron.
With this it is technically possible to translate the relative clause to make it fit:
»X«, »Y« und »z« sind alle/jedes ein Beispiel für ein Oxymoron, was/welches einen kurzen, widersprüchlichen Ausdruck bedeutet.
We have a choice between was and welches. (Das doesn't work here in German any more than that does in English. What would perhaps be borderline acceptable; in colloquial German, was is perfectly normal here.) The problem, however, is that this relative clause is quite unidiomatic. Altogether we are in the fuzzy territory of sentences that are correct enough to be produced by native speakers all the time, but wrong enough to be often rejected by the speakers themselves right after saying them.
Here is the idiomatic way to say the same thing in German, together with the literal English translation -- which I think is also perfectly good idiomatic English:
»X«, »Y« und »z« sind alles Beispiele für Oxymora, d.h. kurze, widersprüchliche Ausdrücke.
‘X’, ‘Y’ and ‘Z’ are all examples of oxymora, i.e., short, self-contradictory phrases.
So in this case you just have less options to say the same thing fully idiomatically in German.