Unless it has changed I believe Alien Night at the bars happen on Tuesday nights. The theme nights can happen even if you haven't been strictly invited to them you just need to trigger them by going to a bar on the night in question. So have your sim go to a designated Bar (the Get Together ones work the best but I have had triggered theme nights happen at bars that I placed from the gallery so it might work at any of them) not a club or a lounge it has to be a bar and the even should trigger to start up for you.
As they said you'll definitely meet them in the science career I actually haven't had many run-ins with randomly discovered aliens in my games lately but I usually ignore the theme nights so that might be why.
You could also create alien families and populate the world with them for your sim to run into. Not as much fun but it would get the job done if the rest didn't happen.
And the Rest of the Nights for those who might be interested.
Daily - Happy Hour
Monday: Bear’s Night (if you have Outdoor Retreat)
Tuesday: Alien Night
Wednesday: Ghost Night
Thursday: Knight Night
Friday: Ladies Night
Saturday: Singles Night
Sunday: Guys Night