Now to the terms:
Tax: Any money the government takes from you (legally) for doing any economic activity is tax. Generally, this is a percentage of the money you receive or give. Taxes are either direct, where the money goes directly from your pocket to the govt's pocket, or indirect, where the money goes from your pocket to someone else's pocket and then to the govt's pocket. (Lemme know in comment if you need further explanation of these terms)
Duty: This is an on-border tax charged on goods (commodities, or things that you can physically touch) either while coming into the country or going out of the country. Generally, a percentage of the value of the good.
Cess: This is a tax on tax, levied by the govt for a specific purpose. Generally, cess is expected to be levied till the time the govt gets enough money for that purpose. The education cess, that is levied currently, is meant to finance basic education in the country.
Surcharge: This is an additional burden to the tax being already levied. Generally, surcharge is levied for a certain period time. For instance, the 10% surcharge being levied on super rich in India for one financial year.
(Surcharge and Cess may look the same, but the difference is in the way of charging. For instance, say some tax is 30%, so out of Rs 100 earning, Rs 30 is paid as tax. Now if the govt levies a 10% cess, the total tax will become Rs 33. However, if the govt levies a 10% surcharge, the total tax will become Rs 40.