Look for siblings, cousins, friends, and neighbors. The Irish tended to cluster by village in the New World. Associate females with male relatives, so you can look up their naturalizations. Yes, but you can access many Irish records here in the US, which you should do before you travel all that way. Consult a general guide to Irish genealogy, travel the Internet.
Many records are available at public and university libraries and genealogical societies.
In addition, the Church of Jesus Christ of the Latter Day Saints has microfilms of Irish records in Salt Lake City. You can order the films from your local LDS Family History Center. You can also write to the various county heritage centers in Ireland to have them search, for a fee, their databases for your ancestors. Spend a few days in Dublin or Belfast first. In Dublin, you can find information at the National Library, the National Archives, and the General Register Office.