There is a Kazimir Rudiak (who is not the one you are looking for because he is 3 years old) listed in the New York Passenger Arrival Lists (Ellis Island), 1892-1924.
His ethnicity is listed as "Austria Polish", which could be useful to narrow down an area for your Kazimir. Generally, Austrian Polish means Hungarian, Ukranian and Eastern Polish. Have you been able to find the Rudiaks in the 1911 census? That should tell you Kazimir's ethnicity and his father's. If it is listed as Austrian, Galician, Hungarian, or Polish, http://www.halgal.com
is good for sources and ideas to do research on those places.
Have you tried tracing Kazimir's route (or that of Michael and Eva) through immigration? Ancestry has decent indexes for ships lists. If you don't have access to Ancestry (try checking your local library or LDS Family Centre for a modified version of their world collection), Library and Archives Canada has images of manifests available, but no nominal index. (http://www.collectionscanada.gc.ca/databases/passenger/001045-130-e.html
). You can narrow it down by year and port of arrival or departure before searching manually. (Since Kazimir likely came from Eastern Europe, try ports in Denmark, Germany, and Belgium first.) Also, since his siblings went to the US, try Family Search for US/Canada border crossing records for all three of them.
Edited to add: Do you have Kazimir's immigration papers? It looks like Kazimer was naturalized as a Canadian citizen in 1932. Library and Archives Canada has a searchable index of people who became citizens between 1915 and 1935 (http://www.collectionscanada.gc.ca/databases/naturalization-1915-1932/001055-100.01-e.php
). His nation of origin is listed as Poland. For $5 you can order a copy of his naturalization papers (http://www.collectionscanada.gc.ca/databases/naturalization-1915-1932/001055-150-e.html),
and that might give you more exact information.
Hope this helps!