Query regarding permission for Indian to work as postdoc in UK
The EEA is the EU plus a number of other European countries (eg Norway) whose citizens have employment rights in the UK. Assuming you're not a dual citizen, option 1 won't apply to you.

If you do not have any reason to assume you are eligible to work in the UK (eg you don't already have a UK work visa) then you should tick opiton 2 - "I am not currently eligible". It is very unlikely that you would have eligibility without already knowing the reasons for it (eg "I already have a work visa").

Then (as @scaaahu says) read this answer to find out how the system works after this point. The important thing to remember is that the university is potentially able to sponsor you to get a visa, so ticking "no" won't stop the application. If they decide to take you, they will be able to take care of the visa issues.

Good luck with the application.