Answer:
1. Hey John! Look at your calendar! Do you know which day is on Friday? That's right, it's my birthday. You know my party would be so boring without you, so I hope you will come and bring that strategic game we used to play last year. The party starts at 5 PM but I hope you will come earlier, so I can show you a new tennis set that my grandparents bought me before other guests arrive.
2. Hey, buddy! You are now big enough to come to my birthday party, as a big boy you are. We will eat cake, play some fun games, draw, and sing many songs. I promise I will learn you how to use my computer, as now you're big enough to play games with me and my brother. I hope I will see you on Friday at 5 PM.
3. Dear Mr. President Obama, I would like to request the pleasure of your company at my birthday celebration, which will take place on Friday (March 27) at 5 PM, at my house (Los Angeles, California). I hope that such an important and great man as you are could find some free time to visit one small boy with huge ambitions and ideals, as my role model and one of the greatest people of the contemporary American history.
Explanation:
In the first case, we can use an informal language, with colloquial expressions, and short sentences, as we are inviting our best friend to attend your birthday party.
In the second case, we should use short and simple sentences, as we are talking to our little cousin who couldn't understand more complicated structures and expressions.
In the third case, we want to invite the former president of the United States to attend your birthday party. Therefore, we should use a formal language, polite expressions, and short, well-structured sentences, in order to show respect and admiration to such an important person.