As to whether it's sarcasm, I'd describe it more as an inside joke with just a touch of the self-aware intellectual arrogance Physicists are famous for (see Lord Rutherford's "All science is either Physics or stamp collecting").

Trying to explain a joke is always dangerous so hopefully what follows won't be a mistake, but here goes:

The way I have always interpreted the first sentence is to hear Fermi saying that when you are doing an experiment, you should have a deep understanding of the family of curves or behaviors the system under test is expected to follow, including the full range of curves that would follow from interactions that are wildly different from what you might naively expect. If you really understand the Physics of the system (this is where it starts to blend the line from advice to a joke), the measurement of one single data point should be enough to tell you which of those possible curves describes the actual behavior of the system (the joke being both that it's funny to be that arrogant and that it's obvious to anyone you'd tell this joke to that mathematically you need at least two points to determine a line, so by saying one point gives you not just a line but a curve the speaker is purposely going over the top for fun). Moving into the second sentence ("two points gives you the distribution about the curve") takes the statement into full-on joke mode, with the comment shifting from an observation about knowing your Physics to an insider dig at the relationship between theoretical Physicists and experimental Physicists (Fermi being one of the greatest theoretical Physicists of all time). When he says that two points gives you a distribution about the curve, he's saying he as a theoretical Physicist understands the underlying Physics of the system better than the experimentalist understands the noise in their experimental hardware, or alternatively that the noise in the hardware is sufficiently uninteresting as to be irrelevant to him. The former view would simply be arrogance but leaving the second option open circles the joke back to include a bit of insider self deprecating humor in that he's purposely ignoring experimental error, a thing theoretical Physicists are famous for doing.