From my understanding, the relationship between the deathwatch and the inquisition, is more like the relationship between the us marine corp, and the us navy. They are closely aligned, and often work together on things, but the inquisition doesnt run the deathwatch.
That's true - for better or worse, FFG has largely decoupled the Deathwatch from the Ordo Xenos, turning what is direct subordination in the GW material into a sort of alliance between equals. For what it's worth, most players here seem to prefer this version, and undoubtedly allows the Deathwatch to be available for a greater amount of missions. I believe the core rulebook even mentions them engaging the forces of Chaos if they should stumble over an incursion just because they still treat their traitor brethren like sworn arch-enemies, so a GM need not feel limited by the retained focus on aliens but could just as well have his players fight all sorts of enemies.
Regarding specific ideas … I don't really know about an Ork-cult (call it "Orkkultism"! this pun is too good to pass up on), but perhaps you could have a tribe of corrupted Feral-worlders ally with an Ork clan to dominate and enslave other humans on this backwards world?
For Necrons, I'd suggest something with mind control … an ancient artifact buried below a hive, invading the citizens' dreams and bringing them to do weird things? You could have random murders and killing sprees, people starting to worship strange metallic totems cobbled together from the scrapyard, or multiple people starting to build components that nobody knows what they'll do, but when combined it's some sort of doomsday device? It gets more interesting when both the local authorities as well as the souped-up gangs start to mess with the Kill-team, which was perhaps sent to this place because the Inquisitor who was there before suffered an "accident", but his last transmission sounded weird …
Or perhaps the AdMech tried to tamper with Necron tech and managed to get their cogitator network "infected", and now your Kill-team has to deal with an ostensibly deserted research outpost which, upon closer examination, turns out to have butchered its inhabitants and now turns upon the Space Marines? Trapping them in airlocks, triggering automated defenses, sending battle-servitors (augmented with bodyparts "harvested" from station personnel) … a good way to add a bit of space horror to the mix. Add some sort of objective like a beacon the team needs to shut down. Maybe the Necrons themselves show up for the showdown, having managed to lock on to the signal with one of their portals, so that the Kill-team must blow the station reactor before the 'crons use it as a staging point for a major incursion…
I can immagine a chaos cult springing up on a planet, but wouldn't that fall more under the responsibility of Ordo Hereticus, or even Ordo Maulas.
The interesting thing is that quite a number of Inquisitorial operations are not so clear regarding jurisdiction, which is why you could have, for example, an Inquisitor of the Ordo Hereticus and an Inquisitor of the Ordo Malleus both investigate the same thing for different reasons - and possibly even coming to blows over it. The various Ordos (and Hereticus, Malleus and Xenos are just the three largest / most influential ones) are just semi-unofficial and optional networks, anyways, so there is no Imperial decree clearly separating what sorts of things would fall into the purview of any single one. As far as the Imperium at large is concerned, there is only the Inquisition - although the Ordos have come to wield different amounts of influence with different factions.