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First, I thought you were talking about customs as traditions))) Then, I understood that you meant customs - as check service on the boarder)) Nevertheless, I found both info about traditions, culture and customs
Finding information in English is just the same as finding info in Ukrainian or Russian just fill in what you need in suitable language.
http://www.geocities.com/ukrcustoms/ - Here is some information in general about Ukrainian customs
http://en.wikipedia.org/wiki/Odessa - as he's travelling to Odessa, here is some info (including places of interest, history, culture etc). On Wikipedia you can also find info about Ukraine - http://en.wikipedia.org/wiki/Ukraine
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And here is info about the customs, where all the luggage is checked -
http://www.ukraineinfo.us/consular/customs.html