You should be able to see Solids and other attributes in object parameters, so you can set up an 'Object overlaps solid' type event.
As for 'point overlaps point', a point is just a co-ordinate with no size or dimension. Two points can only be said to overlap if their X and Y co-ordinates are identical. Due to rounding errors, you might want to round the coordinates to test if they overlap to pixel resolution.
In other words, you can use compare values like so:
+ Round(x1) equals Round(x2)
+ Round(y1) equals Round(y2)
-> Points (x1, y1) and (x2, y2) overlap