How search engines react on specifying the language of a page in the URI?

In the same way as any other url, for example if one page has links with different get-parameters.
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The popularity of the specific page (and hence its position in the results) depends on the distribution of links in and number of external links on every page.

definitely do either a redirect otherwise you will have duplicates and the weight of the pages will decrease, same no /page/1 leading to the first page list and other duplication, the optimizer will first try to remove this crap.

Google in their projects uses the redirect www.example.com/some/path (English) www.exapmle.com/intl/ru/some/path whether on accept-language, whether based on cookies, or session (too lazy to experiment). Page www.example.com/intl/en/some/path there is also (too lazy to experiment whether there is a redirect if headers is sent to a minimum (no accept-language and cook) or issues that have asked in the search results is displayed in English without specifying the language in the url, so it is likely the bulk is given).
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PS they have a 302 redirect is used for this

inclined to the version about redirects and explicit languages in any case, so logical

Actually example.com/en/page.html and example.com/page.html will Staude different pages with different contents, first with the English text, second with, say, Russian, it is normal and does not need any redirects, and search engines you will look quite normal.
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But if both pages, duplicated content, you should choose one URL that will redirect.

at the moment everything works well if we explicitly specified the language to switch to it and keep in kukish, if not specified explicitly, then pull the tongue out of Kuksov, if not installed there is something to pull out of the browser, and if the languages of the browser are missing in the localization is to take the default value. that happens that to the search url without an explicit language will correspond to the default language, as no cookies the search engine does not accept any accept-language headers are not sending.
it turns out that there is duplication. and since the default language can change — you can not tie the absence of language in the URL with a particular language.
It turns out — or redirects or to opt out of the URL with a missing token language (which would not be desirable since it is not always convenient to prescribe this is the token of the language — I must have missed somewhere in the URL, and the user switched the system to another language).

It seems to me that after entering the page, all links must have to give with the required language. Ie you have the maximum indices will be duplicated page of the site, but it is possible to do a redirect.
The Google randomly will not come on site.name/page.html if you are in front of each link to be added to the language.