So to distill the relevant portion of the canonical post (which I still recommend you read):
The use of the past or present perfect implies the action happens relative to something else. The past perfect suggests the action occurs before some other action (which you will subsequently mention) while the present perfect implies the action is still going on.
The phrase "It has just finished" adds a little more emphasis to the just than "it just finished", since it implies the action was going on right up to the present moment. Otherwise the meaning is much the same. Feel free to use either structure as feels appropriate.
That being said, "it has just finished a few days ago" is an odd construction. It should be "it had just finished a few days ago (before something else happened)". The action happened in the past, so (if you are going to use the perfect at all) you should use the past perfect.
I don't think Google is a good resource to judge the popularity of an English phrase since it searches for results with parts of the phrase and not necessarily the entire phrase. Try Googling "it has just finished a few days ago" (with the quotes) and you'll only see three results, two of which are this question. :)