I think your transfromers are manufacuterd by BHEL. If yes nothing to worry because there is no transformer from BHEL without oil leak.
You can Devcon 5 minutes putty and class A putty for arresting oil leaks. But putty is not a solution for many leaks like valve joints, OLCT joints and tank rim...
I think you are looking for online transfer of load. i hope both the transformers are having same no of taps, same impedence and same phase sequence etc.
The best method is adjust the voltage of both the transformer to equal. to be specific measure voltage across volt meter terminals. close the...