Postdoc job inteview presentation - slide "livery" / logos and references?
Typically, in the departments and universities I'm familiar with, as a student you're also an employee of your current institution, benefiting from their space at the very least and participating in the local research culture. As such, it's appropriate to keep the branding on your job talk slides since it's not just some obligation to the university to credit them, but it grounds you in a context of the research at that university. 

Additionally, it's appropriate to keep your acknowledgement slides if there are people to acknowledge. Many PhDs are done as part of a team, and so you shouldn't drop this credit from your slides. That being said, in a job talk, even a short, introductory one, you should concentrate on the parts that you did. You probably shouldn't spend the time reading off all the names and roles of the people who contributed.

Now, given that this talk is short and intended to only be about how you fit the role, it's not even clear to me that you should be treating this as a traditional job talk about your research. I would focus down on the posted criteria and carefully and thoughtfully address how you satisfy them. Presumably you're being given the opportunity later in the interview day to give a traditional academic job talk (i.e. an hour-long seminar), and that's the place where you can dive into your research, credit your team members, funding agency, etc.