Do we need any visa to travel to Goa ?

Citizens of most countries do require a (tourist) visa to travel to India. Kindly contact the Indian Embassy / Consulate in your jurisdiction for more details. A list of Indian missions is available at http://meaindia.nic.in/onmouse/mission.htm.
Registered participants will upon request receive an official invitation letter that might be required for visa applications.

Do we need any vaccinations to travel to India ?

For stay in Goa or any of the major cities, vaccinations should not be required unless you arrive from a country for which Indian authorities need proof of vaccination. If in doubt, please ask your travel agent or the Indian mission in your jurisdiction.

How is the weather going to be like ?

In mid-April, it is summer in India and it will be quite hot everywhere in the country. Temperatures in Goa are more temperate due to proximate of the sea. Though April is generally dry, unseasonal rains might occur in coastal regions. It is recommended to bring light clothing like t-shirts and shorts, and of course swimwear if you fancy a dive in the ocean.

Weather forecast for Goa is available at http://weather.123india.com/goa/goa.html