While various spellings appear in various places, the name used by your family is Dlugoleski will be the names in the United States.No need to worry about the misspellings by census takers, etc.Others immigrating or related may have used Dlugolecki, as indicated by Tad; these are possible relatives but not to be considered without documentation establishing relationship.Perhaps a common relative listed on ship manifests will be found. Using the Steve Morse search engine for Ellis Island can simplify your search, using the sounds like many feature: http://www.jewishgen.org/databases/EIDB/ellis.htmlhttp://www.jewishgen.org/databases/EIDB/ellis.html
Ancestry has ship manifests for other ports and can be accessed at many public libraries as well as Family History Centers.
For 1920, Heritage Quest has Wladislaw indexed as: Dlugoleciti Wladyslaw 32 b. Russian Poland, imm. 1913 CT, Litchfield, Torrington; Daytonville Wife Solastica, 29, b. Russian Poland, imm unknown Children: Yawiga, 7, b. Russian Poland; Genopepca, 6, b. MA; Helen, 4 and 10 mos, b. MA; Matthew, 3 and 10 mos, b. CT;Mary, 7 mos, b. CT.
If you are using Ancestry, plug in Wladyslaw, birth year, Litchfield, Torrington Daytonville, if you can.
Other Litchfield names in 1920: Dlugokenski John 37, b. Poland Litchfield, Harwinton, Harwinton Dlugolecki Frank 37, b. Poland CT Litchfield, Plymouth, Plymouth Twp.
I'll be happy to send you the pages if you are unable to locate them.
Contact the person referenced by Tina, so you will not unnecessarily duplicate research already done.Civil and parish documents are needed from MA and CT for your knowledge.