"invite someone over" is an idiom in English and means to invite someone to come to your house. "have (people / someone) over" is a phrasal verb and means again to invite people / someone to your house. E.g. My mom doesn't let me have my friends over for the weekend. So "over" is a part of these two phrases and cannot be explained separately.

Hell Amir: It is just a common American colloquialism. It is a term that has become an accepted use. If someone comes "to" your house, therefore, they are said to be coming "over to your house". It means something equivalent to; "My friend is coming "over" or across--the---street, to my house."---Warm Regards, Bruce

"Over" indicates a transit across a distance: from their places to mine. You definitely need it in your second sentence. Your examples work as phrasal verbs: invite (sb) over; have (sb) over.

Hello Amir: You can simply remove the word "over" and the sentence will have the same meaning, and be grammatically correct also. Using the word "over" as in the original text, is entirely superfluous. ---Warm Regards, Bruce

Let me ask another question. What would happen if we omit the word "over"? Does it change the meaning?