Alright....i'm a bit confused on the whole handicap thing when playing a match between people with different handicaps on different set of tees from different courses.

Example:

Myself: 2.2. handicap at home course playing back tees
Par Rating Slope
67 68.0 114

Dad: 8 handicap at the same course as me playing middle tees
Par Rating Slope
67 66.9 112

Grandfather: 16 handicap at a different course playing middle tees
Par Rating Slope
71 69.3 123

Now we are playing a match at my grandfathers course. Both my dad and him will play the middle tees and i will play the back tees.

par rating slope (from back tees at grandfathers course)
71 70.5 126

How do i go about calculating handicaps to play a nice competetive and even match?

It depends. Are the handicaps you listed USGA handicaps, or course handicaps?

Assuming they are USGA handicaps, you'll use the slope of the tees you are playing to find your course handicap. For you, your course handicap would be 2.2 X 126/113 for a course handicap of 2.5. Your dad is 8X123/113=8.7. Granddad is 16X123/113=17.4.

Then round your handicaps to the nearest number. Yours=3, Dad=9, Granddad=17.

Since you are playing different sets of tees, you'll use the rating to determine how many extra strokes you'll get. In this case 70.5-69.3=1.2, so you round down and get 1 extra stroke for playing the back tees.

So you'll be giving Dad 5 strokes, you'll be giving Granddad 13 strokes, and Dad will be giving Granddad 8 strokes.

Since we don't know what dad's and grandpa's index is - just assume the 3 players are 3, 8 and 16 handicap.

When you play at Grandpa's course, you should play as a 3, dad and grandpa at 7 and 15. You could also play as a 4, with dad and grandpa at 8 and 16.

No way to do it accurately without their indexes, but if you have them, use Krusty's formula above and either take one shot away from them, or give yourself one more, (after the calculations).

(index) X (slope) / 113 . round 8.4 down to 8, round 8.5 up to 9. Now you have your handicaps. Then use the course rating to add or subtract strokes given.

I see the USGA way of doing things is again a little different than the EGA way.
The standard formula is
(HCP + CR - Par) * Slope / 113 = Course hcp
Essentially the same as USGA, but in one formula ;-)

This would return for your example:

You: 1,89 = 2
Dad: 6,85 = 7
Gramps: 15,56 = 16

As you plan to do match play the shots given will be as follows (75% of the hcp difference):
You - Dad: 4 shots
Dad - Gramps: 7 shots
You - Gramps: 11 shots

Enjoy your match!