All these sentences are correct, but as you say, their meanings are slightly different.
There are two things we always need to keep in mind when reporting speech:
- The context of the actions or opinions in the moment we report them (are they still true?)
- The relationship between past events (in a sequence, simultaneous, or cause and effect)
"He told me that the road trip has been cancelled."
In this example, the road trip was scheduled for some moment that is still in the future. You use the present perfect to show that this action (being cancelled) has an effect on what happens next. That is, you won't go on the trip. Actions in the perfect tenses have an effect on what comes later.
"He told me that the road trip had been cancelled."
In this case, the road trip was scheduled for some time in the past (in terms of the moment you report this speech). Again, we're seeing the perfect tense which means there was an effect on what happened next. For example, it had been cancelled, so you made other plans. Or, as The Photon explained above, it could be that this changed later.
"He has told me that the road trip has been cancelled."
This construction is a little less likely (at least in U.S. English), but it's quite close to the meaning we just discussed in the first example you proposed. Again, as The Photon says, you're being imprecise about the moment you were given this information. You're focused on the information and what it means to you (its effects), which is why you're using the present perfect.