How effective are Psychometric Tests and Assessments as a recruitment tool? How should they be used? And what positions should they be used for?

The validity of recruitment tool in isolation are generally less than0.5 statistically.
Hence using a Psychometric instruments along with other recruitment tools - interview or Assessment centres( wherein Psychometric is one of the instrument widely used) improves the 'validity' of your recruitment process phenominally (>0.5).
One of the tool that i use & widely used by HR Fraternity is DISC Analysis -Human Job Analysis & People Personality Analysis developed by Thomas assessment International.
I feel this tool should be used for all critical positions ( irrespective of job level)in the organizations.
My suggestion would be you need to develop certified assessors internally ( both from HR & business) through Thomas Assessment /SHL or DDI consultancy.
Note: Pychometric tool by itself should not be made as a selection/rejection mechanism and should be be adminstered by certified member.

I would suggest you to try a test CTPI-R by central test if you are looking to hire in the senior/mid level management ..for freshers I think psychometric assement will not be ideal you can try aptitude test instead.