What does that party entails? Do you have to control themselves or are they AI controlled, is it turn-based or what, etc.?

IMHO the combat in classic computer RPGs is usually some kind of strategy mini-game in itself (e.g. Betrayal at Krondor, Baldur's Gate etc.). The fact that the combat is handled that way is not what makes the game a RPG. It could just as well be a party RPG which is completely in a first person view in real time and your party members are controlled by the AI, and you shoot enemies like in a FPS game. It is still a party-based RPG, with no strategic combat.

Depending how much the gameplay (combat) relies on either strategy or action, many people call some RPGs "strategy RPGs" and some "action RPGs". I recall e.g. Final Fantasy Tactics being called "strategy RPG", ie. an RPG with heavy emphasis on strategic gaming, even more so than main Final Fantasy games.

To me, hack clones (Nethack, ADOM etc.) are close to purest form of RPGs, as there your character traits (stats, how you have equipped them etc.) matters the most in surviving the challenges in the game. You can use some strategies in e.g. combat to try to turn things your way (e.g. waiting for several enemies to be in line before zapping them all with your magic wand), but overall there is less emphasis on strategy than on other classic CRPGs where you can sometimes alleviate your character weaknesses heavily by strategic thinking in combat, being able to kill much more powerful opponents early on than you were maybe supposed to.

tl;dr:

In a strategy game your strategic thinking skills (in the combat field etc.) are what matters the most in how you do in the game.

In a RPG it matters the most to your success how well you have developed and equipped your character over time, and you have to rely on your character's traits to survive (e.g. you wouldn't necessarily put a strong negotiator in a boxing match, unless you believe you can win it by talking).

Worms series?

I think it's really difficult. The border between the genres are too fuzzy to explicitly isolate traits, or even a set of traits that defines a genre. Which isn't surprising because genres have been defined through hundreds of previous associations, and developers aren't bound by what is considered to be an rpg/rts or whatever when they make a new game.
You'll just run into endless problems trying to isolate traits, because someone will almost always be able to give counter examples. Your experimental strategy definition already includes several rpg games. For example the infinity engine games. You have to be very mindful of where you place your party members, for example to control enemy aggression, to avoid/exploit bottlenecks and to avoid/use aoe spells.
Your experimental action definition also describes System Shock 2, though nobody considers that to be an action game.

I think the best one can do is to give a very vague description and then include examples. Eg:
The RPG genre refers to games with an emphasis on player character development, like Diablo, Elder Scrolls and Ultima.
and to tacitly concede that the definition isn't perfect, and that it doesn't matter that it's not perfect.