AA codeshare with Aer Lingus AFAIK, they use Aer Lingus planes, so should cost more normally for the same thing. AL are to codeshare with Jetblue from this Summer ( they are on the JFK-ORD route AFAIK also), so you will be able to book onward flights through Al site from then. AL are the only ones I know that fly direct to Chicago. ATA, Midwest,Continental, Delta, United, US Airways go from JFK to Chicago airports (ORD, MDW, MKE), Continental (via Newark) and Delta ( JFK and Atlanta) do flights from Ireland,United also to Philadelphia, Canada'a main airline does flights to Toronto in Summer also, so check connecting flights from those hubs firstly with those airlines, and later via lowfares ones,
www.kayak.com is handy for US low fare airlines.
Don't forget that Chicago is very well connected with train routes, if you want to see some of the country going there from New York, Boston, Toronto etc.