Brad's given a pretty good explanation of interrupt/disturb. As for "world" - well, the L is always pronounced. As for the R, US speakers will always pronounce it. UK/Australian speakers have a different rule for pronouncing R in that situation, and to the listener it may sound soft or nonexistent (don't just drop it - we have a rule, remember). The actual pronunciation of the letter R also differs between styles - don't assume any are like the R that you know.

There are no silent letters in the word "world"--we pronounce all of them. To interrupt means to insert yourself into someone else's action or speech. To disturb is more general: you might disturb someone who was reading, or watching TV, or just thinking. In this sense, an interruption is a more specific form of a disturbance.

I agree with Brad