So, I was wondering if this would work. 

My dhampir bites an unconscious person. A friend who lets this happen persay. 2d4 (Crit) averages to 4 damage, blow a superiorty die, 2d6 averaging to 6 damage, plus 4 due to strength bonus, and home rule for called shots adding 5 damage, totaling to 19 total damage. This adds to my next check or attack roll. 

This means my next attack roll/check, would have a +19 and x default bonuses. 

Does this check out? 

The average of a d4 is 2.5, not 2, and a d6 has an average of 3.5. Vamparic Bite uses your Constitution mod instead of your strength per the abilities description, so you would deal 2d4+2d6+constitution modifier damage. This would add up to 12+con mod damage, plus whatever "called shots" damage is, assuming that it also deals piercing damage. If you Con mod is four and "called shots" does indeed deal 5 piercing damage, then you would get +21 to your next roll, not +19.