i am at the part where you have to get rid of the nightkin in the basemant at the repconn headquarters. when i went to talk to davidson i said i would help get the stealthboys then i unlocked the door to where harland was and i offered to help find his friend. i couldn't find the stealthboys and i was getting impatient so i killed davidson and i killed all the other nightkins then i went searching around and found harland's friend and told him the bad news. when harland let me look around his area i couldn't find anything but a computer that talked about the shipment of stealthboys. i figured since i killed all the nightkin i beat it but when i went to talk to jason i couldn't tell him i get rid of them and the only option i had was "i'm still working on it".
i think im stuck and i don't know how to fix things.
what can i do? i don't want to start the game over.

You have to kill all the Nightkin. I checked the wiki to see the exact number, but I didn't see it listed. The game probably counts how many you have killed so you have either missed one, or the game glichted counting and you're screwed unless you're on PC. So either muck about down there to see if there are any more SMs or if you are on PC just console spawn a few more SMs to up your kill tally. That's what I used to do in FO3 when this would happen at the Jefferson Memeorial and I'm sure it will work here also.

-Gunny out.

It did the same thing to me, so what I did was get a [censored] load of mine and made bottle cap mines and left for a bit, and then while I was about to lay waste to the Deathclaw Mother, 50xp appears, and just after I waste her another 50xp, it was quite funny.
Then I went back collected any unused mines any talk to the bright ghoul leader and then he told me to go to the launch site.

So try that, and if it doesn't work send me a message saying what platform and how many hours you have played and I will try to make a sort of mod to get around it, OK?