Visas weren't required until the Immigration Act of 1924 (which took effect on July 1, 1924).

If your relatives naturalized after July 1, 1929, there is likely a photo attached to their Declaration of Naturalization (per Naturalization Act of March 2, 1929).

Regards,
David Oseas

Researching:
HYMAN/HEYMAN/HEIMOWITS/CHAJMOVITS: Zemplen-Dobra, Hungary > New York
KLEIN: Satoraljaujhely (Ujhely), Hungary > New York > Los Angeles
KRONOWITH: Hungary > New York
OSEAS/OSIAS/OSIASI/OZIAS: Iasi, Romania > Chicago > Milwaukee > Los Angeles
SCHECHTER/SHEKTER: Kishinev, Bessarabia > New York  
SHERMAN: Iasi, Romania > New York > Los Angeles
STRUL:  Iasi, Romania > Haifa, Israel
WICHMAN: Syczkowo (Bobruisk), Belarus > Milwaukee > Los Angeles