(C) is a little more complicate, so let's start with the difference between (A) and (B). I think the easiest way to explain the difference is with a graphic. Imagine the Y axis of a graph, where each (-) is some measurement of time. (A) The Beatles have influenced a lot of musicians, means this: -The Beatles made a band. - -The Beatles influence a lot of musicians. - -The Beatles influence a lot of musicians. - -The Beatles influence a lot of musicians. - -Present day. ...You get the idea. It's something that happened in the past, but it happened more than once, and/or over a long period of time. (B) The Beatles influenced a lof ot musicians, means this: -The Beatles made a band. - - -The Beatles influence a lot of musicians. - - -Present day. So this is different, (B) implies that something happened one time, and then it was done. So when you use (A), you're talking about a long period of time where the Beatles had influence on different musicians at different times, through a long period of time. Because the Beatles really DID influence many different musicians at many different times, it makes most sense to use (A). So when you change it, and use (B), it means something different. Because this was a continuous action that took place over a long time, using (B) implies that you're talking more about the EVENT or PHENOMENON of the Beatles having musical influence. You're talking about all of those different events as one TREND, because this is the tense that we use for something that happened ONCE. Like I said, (C) is complicated, because it's more removed from the present. This is hard to explain, but you might use this tense in the following example: "The kids decided a band. The band sounded a lot like the Beatles, because the Beatles had influenced a lot of musicians." So, when you're using the past tense to describe something, and then you need to talk about something that happened BEFORE what you're describing, you would use this form.

Let us call "influencing a lot of musicians" the result which the Beatles caused. When you use "have" it means the result was caused over a period of time leading up to the present. Take this example: "I have only ever eaten two kiwis in my life so far." You could be saying you ate one once when you were a kid, then another many years later. OR, you COULD have eaten both on one single occasion and then never again. In that case, you could also say "I ate 2 kiwis one time 5 years ago." Here's the key: "have" is used to talk about what happened "since" sometime in the past up until the present. If you did something over a extended period of time starting in the past and ending in the past, you would still say you "did" it during that time e.g. "I ate 2 kiwis (while I was) at summer camp" Now, contrast this with: "I have only ever eaten two kiwis in my life." Both statements can be true. "have" is essentially saying: "as of today, as of right now, at the present time, i have done these things since that point in the past..." The plain past tense just says you "did" something at ONE period or point in time in the past. It doesn't matter how long that time period is, just that it doesn't extend up to the present: "I ate only 2 kiwis over those 5 years." "had" is simply the past tense of "have", so instead of referring to a time period leading up to right now, it refers to a time period leading up to a point in the past. These examples should help: "I ate kiwis for the first time in my life during summer camp." "Since summer camp, I have not eaten a single kiwi." "Until summer camp, I had not eaten a single kiwi in my life." To go back tot he original example, [a] means the Beatles' influence is still felt today [b] means they made an impact in the past, but their influence may OR may not still be felt today [c] means by some point in the past, the Beatles "had already" influenced a lot of musicians.

A - tells us that the Beatles have influenced musicians in the past up to the present day. B - tells us that the Beatles influenced musicians solely in the past. C - tells us that the Beatles influenced people in the past, but it implies a delimitation that is expected to be explained along with the statement.

(a) This gives the idea that the Beatles did the action of influencing in the past, and their influence continues today. (b) This gives the idea that the Beatles did the action of influencing in the past, but their influence is not significant today. (c) This does not sound correct. I think you could use "had influenced" like this: The Beatles had influenced a lot of musicians before Led Zepplin became popular.

A) tells us about the present. B) & C) tell us about the past, but C) is not complete. You need more information here. You can look up "present perfect", "past simple" and "past perfect" and examine the differences that way.