Simple script with no interface to quickly align points parallel to any orthaginal axis with one touch of a key.
The script works out which axis the selected points are closest to being parallel to then moves them to the average of their positions along that axis.
If the selected points are already aligned in one orthaginal axis it will align them on the next closest
run it 3 times in a row and you get all points at one position
Some examples
BEFORE ...................................................................................................................................................................AFTER