Hi, I am sorry but don't have access to many USA records but had a quick look to see if there were any hits on the name, there are no VLODYKA but there are a handful of WLODKYKA
Incoming passenger lists to UK on Ancestry
first date birth, 2nd arrival, port of departure, port of arrival
Maria Wlodyka --- 30 Oct 1909 Montréal,Québec,Canada Liverpool, England
Wasyl Wlodyka --- 30 Oct 1909 Montréal,Québec,Canada Liverpool, England
A Wlodyka 27 abt 1876 26 Jun 1903 New York, New York, United States Liverpool, England
Louisa Wlodyka 23 abt 1881 Jun 1904 Boston, Massachusetts, United States Liverpool, England
Bronislawa Wlodyka 45 abt 1902 26 Sep 1947 Bombay, India Southampton, England
Bronislaw Wlodyka 33 15 Jan 1925 3 Nov 1958 New York, New York, United States Southampton, England
Leokadia Wlodyka 18 abt 1929 26 Sep 1947 Bombay,India Southampton, England
Jozefa Wlodyka 27 10 Feb 1931 3 Nov 1958 New York, New York, United States Southampton, England
Maria Wlodyka 7 30 Aug 1951 3 Nov 1958 New York, New York, United States Southampton, England
Tadeusz Wlodyka 4 23 Apr 1954 3 Nov 1958 New York, New York, United States Southampton, England
Sorry its not much but you never know
NJO in Cornwall UK