Webway STRIKE & Screaming Jets

If my army includes both a Drukhari and an Asuryani Detachment, my understanding is that, for example, an Asuryani unit could use the Webway Strike Stratagem and a Drukhari vehicle use the Screamig Jets Stratagem?

I don't see a reason why not, but maybe this has come up in a FAQ I'm not aware of.

There is an FAQ that says Stratagems with the same name from different books count as being the same. However, a combination of Webway Strike and Screaming Jets or Webway Portal and Cloudstrike seems legitimate.

This is indeed true.
You could have a single army of three Detachments using Webway Strike, Assault and Portal.

9 CP, 2*12 Troupes, 2*20 Kabs with 4 Blasters, 2 Splinter Cannons and 2*20 Guardians with 2 Scatter Lasers.

Fun.