The short answer is yes.
Here is the description to the Backstab skill from Rikimaru
If Riki attacks from behind, bonus damage is applied based on his current agility.
That said, all attacks from behind will do extra damage that can be calculated (ignoring armor resistance) by adding the ammount added to the base damage from your character.
Here is some information about how Critical Strikes work:
Critical damage is physical damage and reduced by various types of armor. The red number shown by critical strike is displayed before reductions (this is why illusions don't show very low red numbers). Critical strike does not work against buildings and is subject to pseudo-random distribution. Because critical strike multiplies the attack damage of a unit, it is a scaling ability (unlike the damage of Monkey King Bar's mini-bash ability).
Backstab and critical strike can proc in the same attack. Period.
What's not clear here is when will the critical strike bonus be calculated.
The backstab skill adds bonus damage to your atacks based on your agility, and critical strikes have a chance of x to multiply by y your atack damage.
Lets say critical strike damage is the last parameter to be calculated. That would lead us to something like this ( I picked the values )
Attack Base : 50 , Backstab Bonus : 40 , Critical Strike Multipler : 2
Total Damage = (50 + 40) * 2 = 180
On the other hand, if Backstab bonus is added after the Critical Strike sums up, we would end up having :
Attack Base : 50 , Backstab Bonus : 40 , Critical Strike Multipler : 2
Total Damage = (50*2) + 40 = 140
TL:DR
Whether the Critical Strike is calculated after or before Backstab sums up, is not clear, but they CAN proc in the same attack.
Best Answer
Short answer: No.
Long answer:
Double Damage runes take into account only pure hero damage and attribute damage items (except for pure damage items like Divine Rapier).
They do not stack for other damage increasing abilities (Earthshaker and Enchant Totem, Sven and God's Strength etc).