Intercepts and aerial combat in IMC (or my no-fly zone is full of clouds?!)
In the first scenario, where it sounds like you're assuming that the intruder aircraft is known to be hostile even without seeing it, a shot with a radar missile would be unaffected by the IMC, and that scenario is a pretty straight-forward kill.

The hard part of IMC for a modern fighter aircraft isn't killing the target, it's getting the positive ID on it that's necessary before shooting in order to assure the chain of command that you aren't, in fact, about to kill a neutral or friendly aircraft who's wandered into the wrong place at the wrong time with the wrong squawk.  THAT is where VMC becomes necessary, in most cases, to get the required visual ID on the target.

Using radar alone, an interceptor could close to some reasonably short distance (say, inside a mile, with some altitude separation as well), and if the unknown aircraft enters VMC even briefly, then the intercept could be completed to the point where one interceptor makes the visual ID.  With the aircraft being known to be hostile, that interceptor could break away, and a wingman, maintaining position further back, could then take the shot with a radar missile.

Presumably, the "bad guy" has some mission to complete, and most of those (though not all) tend to need VMC to accomplish -- dropping bombs or taking photos or whatever.  So chances are probably pretty good that the intruder is going to get to VMC eventually.  (Or, if he drops bombs off of radar/GPS, then that act itself might be sufficient confirmation of hostile intent that the interceptors would be cleared to engage, ensuring that the bandit doesn't live to ever repeat that mission.)