It has been said that the history of the Ulery's must be tied to their religious beliefs.There is some consensus stirring that says they emigrated from Germany to the US likely through the port of Philadelphia motivated by religious persecution in the German region and religious freedom in Pennsylvania promised by its owner, William Penn.
It is thought by some that the Ulery's or Ulrich's were Dunkards, a sect of anabaptists believing in 3 successive submersions for baptism and rejecting the infant baptism practiced by many mainline Protestants, most pertinent, the Lutherans.The Dunkards established themselves in Penn. and have spread in small numbers to other nearby states.
Though the group has not spread its beliefs far, there has been some association with a mission in S. America.Classified as Separatists, they are in this sense brothers of the Menonites from which come the Amish.
It may be useful to discover the religious affiliations of your Ulery relatives.Some church groups keep death records, membership records, marriage records and such.
I cannot say that the religious or even ethnic lineage of the Ulery's is unequivocally confirmed.You may want to use the above as more of a guide than as fact.