What are the methods to measure distribution transformer vibration in 0.5g range?
If you google "optical displacement measurement vibration", you will find several potentially useful references.  For example one system uses optical fibers to measure vibrations, as shown below.  Optical sensors are  immune to electrical interference.



While commercial sensors are expensive, you could perhaps make something yourself with a laser, a mirror, and and a DVD diode sensor.  Here is a link to a paper that uses a laser pickup as an accelerometer, as shown below.