Using "every" with several objects

It depends on the context. If you already used the word "every" a lot (before your sentence or after), you might want to go with the first one (to avoid repetition). Otherwise, it is okay to go with the second one.

"Every", like its partner "each", is a singular pronoun. It's singular even with a list of groups, because "every" makes you consider each member of each group individually. As such, you should always use a singular verb when "every" is part of the subject.

Every American, Australian, and Canadian speaks English

and

Every American, every Australian, and every Canadian speaks English.

both have correct subject/verb agreement (even if they're both factually wrong). As stated by @Davo in the comments, the form with all the "every"s simply adds emphasis.

If you want to use a plural verb form, use the plural pronuon all:

All Americans, Australians, and Canadians speak English.

or

All Americans, all Australians, and all Canadians speak English.