There is a myriad pages and blogs out there with interview advice, so I won't bother to give tips here. What I will say though is that I was invited to several PhD interviews (both PI interviews and funding interviews) and that pretty much all of them seemed to follow the "stress interview" path.
Of course it might just be my personal impression, but all official interviews were panels interviews, with people asking unrelated questions in quick succession, frequently forcing me to forget about my current train of thought and jump onto a completely new, seemingly random (as in: not following from the previous question/answer) idea. Some questions were relatively easy and predictable - about me, my current research project, ideas, experience. But there were also questions about aspects of methodology and analysis for the PhD project (which I would be starting in 7-8 months time) and let's face it, it's pretty much impossible to know details of those this far in advance, while applying for several projects. There were questions of the predicted impact of the PhD project, how it would change the field, what post-doc projects would I like to create based on the PhD outcomes... Again, that's about 4 years from now. Those big picture questions, asking for a lot of detail were probably the hardest, although I was also asked a bunch of modelling questions despite the fact that I clearly stated in my application I have no modelling experience.
During one of my interviews I gave a 3 minute presentation on my Masters project - and afterwards I was left there hanging, the questions started without any indication I should sit down with the panel (I figured what the heck and crossed the room and pulled a chair for myself). After some of the answers I gave I was told "this is not what I wanted you to say".
I also had at least one "mean" interviewer on each panel, one person clearly disinterested in me and my answers, interrupting or looking out of the window. I was incredibly grateful that someone warned me about this type of behaviour before my interviews. Once I spotted it and knew I can safely assume it's just an interview method, paradoxically it calmed me down instead of adding stress - I expected it to happen, it happened, therefore things were going how they were "supposed to" go. I knew it wasn't personal and it helped.
The hardest part of the process ironically turned out to be linked to the fact that I was made more than one offer and had to make a choice. And I wanted it all.