You know, it would make questions like this
much easier if people would provide references for where the feats can be found.
Sneak Attack and Skirmish are entirely different powers and operate completely separately.
Since neither Scout nor Ranger grant any Sneak Attack, and since none of the feats modify this, the character you describe has Sneak Attack damage of +4d6 (7th level Rogue).
Per the effects of Swift Hunter and Swift Ambusher, the character's Rogue and Ranger levels both stack with his Scout levels to determine Skirmish bonuses. So he effectively Skirmishes as a 15th level Scout - +4d6 damage/+4 AC.
Per Improved Skirmisher, if the character moves 20ft away from his start position (rather than the normal 10), his Skirmish bonuses increase to +6d6/+6 AC.
As noted, Sneak Attack and Skirmish are two different powers with two different triggers. Therefore, on any given attack the character may qualify for both, one, or neither.
If both Sneak Attack and Skirmish apply, he gets +8d6 damage and +4 AC (+10d6 and +6 if Improved Skirmish also applies).
If only Sneak Attack applies, he gains +4d6 damage and no AC bonus.
If only Skirmish applies, he gains +4d6 damage and +4 AC (+6d6 and +6 if Improved Skirmish also applies).
And if neither applies then he gets no bonus damage or AC.
I hope that helps.
