Pretty much all curves in Inkscape are basically cubic Bezier curves. For your example with the four points, first make sure your Bezier tool is set to 'Create regular Bezier path' () and add a line connecting P0 to P3:
Then shift-drag the nodes with the node-tool, adding handles to them, and drag those to points P1 and P2 on each side:
As for quadratic curves, I don't think there is an easy way to draw them with Inkscape's drawing tools (there is a BSpline-mode, but that's not quite the same). However, you can use the 'Edit → XML Editor...' to manually edit the path-data in the
d-attribute, entering your coordinates and using the 'q/Q' commands:
In this example, the
m 100,80 part is the coordinates of P0, then
Q 222,106 for P1 and the last pair (
311,-31) is P2.
By the way, this method also lets you directly specify cubic curves with the 'c/C' commands (e.g. something like
m 100,50 C 150,50 150,200 50,200).