Can you give a link or something for Death Strike? I'm not seeing it anywhere.
Are you talking about class other than Assassin? B/c there isn't a Death Strike there.
No, they don't stack. Abilities that stack across class say so, and the special abilities for PrC's and normal classes don't use the same formula when DC's are involved.
The way it is written, no your Rogue levels do not stack. There is nothing in the description of the attack that would imply it even a little. This does have the consequence of making the save DC for the death attack incredibly low (at early levels).
You may be able to convince your GM that the death attack save DC should scale based of 1/2 character level (not class level). Your save DCs would end up at the same possible maximum, but would progress more regularly. You wouldn't end up with the save DC being 11+int at Rogue 5/Assassin 1 nor would you end up with it being 20+int at Rogue 5/Assassin 10.
The Assassin is not that good. You can make a better "assassin" without the PrC if you ignore the one hit kill.
It is also more of an NPC class, so it works ok in that regard by not forcing the PC's a chance to have to make a super high save.
Yeah...it'd actually be pretty terrible (for game balance) if a character with a death attack like that could easily get it off with a high DC. The universe would just be full of assassins ganking everyone with the targets having a very low chance to save. It would mean a GM could never send an assassin (of the PrC) at players without the expectation of actually killing them.