Do I need a trasit visa for a layover in Delhi ?

You'll probably want to contact the nearest Indian embassy or consulate office to you to ask them what the specific rules are, as there is a lot of conflicting information online regarding the requirements for a transit visa in India. The first website linked below says that a visa is only required if you would have to leave the transit area for any reason (such as having to claim and recheck luggage), but the second website has several people who claim that the transit visa isn't necessary. If you find it difficult to determine from the embassy what the rules are, you may simply be better off buying the visa even if you don't need it -- the $50 or so that you'd pay for the visa is far less than the cost of changing your tickets if you are denied boarding at your origin because of the lack of a visa.

With respect to the transfer of your bags in Delhi between Asiana and Jet Airways, whether this will happen depends on whether there is an interline baggage agreement between these airlines. The fourth link below indicates that Jet Airways has an interline ticketing agreement with Asiana -- typically, the ticketing agreement also extends to baggage as well, but you'll likely want to confirm with Asiana and Jet Airways that they do, indeed, have such an agreement for baggage.