Wagn strips out most classes from HTML. But it will leave in classes that begin with "w-" so for example on my wiki I use the class "w-gray" and then have CSS style those things gray.
To be clear, Wagn strips out most classes, but not from HTML cards (those with the HTML type). Most other cardtypess (including Basic) will strip extra HTML. I don't know what you mean by having set Episode card to HTML. A card can only have one type; it can't have both the Episode type and the HTML type.
In addition to John's workaround, there are at least two others:
1. You can include an HTML card inside the Episode card where you need the special classes
2. You can add a structure rule to the Episode card (one that applies as narrowly as only to the one episode card if necessary), and that structure rule can be an HTML card.
Okay, so I go to the base card for the Episode cardtype. I go to Advanced > Rules > All Episode Cards. There's a "default" option, and when you open that you can select a type. It was Basic. I changed it to HTML. I have no idea what that setting is actually supposed to do, but it seemed like the best way to say "hey, Episode cards should act like HTML cards not Basic cards".