What is the difference between the following sentences:
He may have arrived now.
He might have arrived now.
He could have arrived now.
In all three cases I would be more likely to use "arrived by now" (his arrival was at some point in the past) or "arrived just now" (his arrival was in the immediate past) rather than "arrived now."
With this sentence, where we're discussing the possibility of his arrival, the three are interchangeable and have nearly identical meanings. Some people use "might" for cases where an even is unlikely and "may" for cases where an event is likely, but there is no definite rule there. "Could" is literally stating that his arrival is not impossible.
Here is a discussion of May vs Might that is well written and clear that might help you. (I could have written "could" or "may" in place of "might" in the previous sentence and it would have meant the exact same thing.)
This question has actually be asked multiple times on the English Language Usage Exchange as well.
At the very least, know that in using these words to express probability, not even the people who speak English as their native language are sure which to use.
These sentences aren't contextually correct. You've used the past-tense "arrived" with "now," which indicates the present. If you were to say "arrived by now" that would be different, because "by now" indicates time that happened before now (the past). This is the most common turn of phrase. You may also use "just now," which indicates some short period time that has just passed (i.e. a second ago, a minute ago).
Now, to get to the difference between these verbs.
He may have arrived by now.
He might have arrived by now.
These are just about the same in this context. Normally, "may" is used to indicate someone is allowed to do something, usually by societal standards or rules. "You may now board the plane" indicates that there was a rule prohibiting passengers from boarding the plane before, and that rule was lifted.
When "may" is discussed in the context of an event happening, however (i.e. the arrival of a person), its definition changes to be similar to "might;" that is to say, it is possible that he has arrived, but I am not certain. These two words both imply that there is a substantial chance that the event has happened already. "Could have" is slightly different, in that it only acknowledges the event has possibly happened, but makes no implications as to how likely it is. "Could" literally means "capable" of something, so it only acknowledges that he is "capable" of arriving. That doesn't really connote or imply that he already did.
These are very minute differences and would almost certainly go by un-commented on in colloquial conversation.