Polearm Gamble's attack happens before the enemy moves adjacent to you.
From the PHB, p204 (emphasis mine):
When a nonadjacent enemy enters a square adjacent to you, you can make an opportunity attack against that enemy.
So Polearm Gamble's attack is an opportunity attack.
From the RC, p246:
Opportunity attacks use opportunity actions.
From the RC, p197 (emphasis mine):
Interrupt: Just like an immediate interrupt, an opportunity action interrupts its trigger, taking place before the trigger finishes.
Opportunity actions take place before their trigger; therefore Polearm Gamble's attack takes place while the target is still 2 squares away.
Booming Blade can hit.
I'm not sure what kind of crack the Character Builder is smoking, but Booming Blade's range is Melee: Weapon per page 27 of the FRPG. Thus, as long as you're wielding a reach weapon (like a glaive), Booming Blade is a melee 2 attack.
Note, though, that Booming Blade requires the target to start their next turn adjacent to you to take the extra damage, so if you use it during their turn with Heavy Blade Opportunity then they won't be at risk until their next turn.
Luring Strike needs help to slide the enemy.
From the RC on forced movement, p212:
Distance, Specific Destination, or Both: The power or other effect that produces forced movement specifies a distance in squares, a specified destination square, or both for the movement.
...When a destination is specified, it is absolute; the creature or effect must either move the target to that destination or not move it at all. Often a destination is combined with a distance, which means the target can be moved to the destination only if it is no farther away than the specified distance.
Luring Strike specifies both a distance and a destination; if the distance isn't enough to reach the destination, then you don't slide the target. Since the target will be 2 squares away when you make an attack with Polearm Gamble, slide 1 won't be sufficient to get the target to the required destination. If you have something to increase your slide distance (such as the popular Rushing Cleats), however, then you'll have enough slide distance and will be able to move the target with Luring Strike.