How do I measure for a table top inside a (slightly irregular) nook/alcove?
One of the simpler ways to do this is with a framing square (a good tool to have on hand).



You need to measure the top at the height where the tabletop will be. Mount cleats (long strips of wood running horizontally) to hold up the top along the three walls. Cut the two side walls a bit short so the cleats do not show once the tabletop is in place.

Now it's time to measure for the top.

Start with the back wall. Measure its length and draw on a piece of paper. It doesn't need to be full size or strictly to scale. Put the corner of the framing square into each of the back corners. Choose the corner that allows you to get the square's corner into the wall corner. Measure the length of the tabletop along the side wall. Be sure you indicate the measurement at the actual point of the edge of the tabletop, not the end of the cleat, which may be shorter.

Have the 24" leg pointing outward. There will be a gap between the end of the square furthest from the back wall and the side wall at the outside edge of the planned top. Measure that gap and transfer it to your drawing. 



Flip the square and do the same thing for the other corner. But this time the end furthest from the back wall may have a similar gap to its side wall. Or it may be square. Or it may have a gap at the back wall. Whatever it is, measure the length and the gap. Transfer the measurements to the drawing.

With measurements of the back edge, the side edges and the gaps, you can lay out the exact dimensions on your tabletop material. While theoretically you do not need to measure the front edge, it couldn't hurt and it will serve as a check to indicate that your other measurements are correct. If you carefully record the measurements, the angles will take care of themselves. 

If you want to be super sure, transfer the measurements to a cardboard pattern and fit into the space on the cleats. You can fine tune the pattern before cutting the final material.