I don't even see a pl_PL file in the EventCalendar module. Did you create one?

Yes I did. Now in lang dir are en_US.php de_DE.php and pl_PL.php . I did translations basing on en_US.php
and it works on almost whole calendar interface beside $LiveCalendarWidget and $CalendarFilterForm.
So I'm trying to solve it.

Found the problem. First, update your SVN to get a new LiveCalendarWidget.ss

Then, make sure your entry in your lang file is:

$lang['pl_PL']['LiveCalendarWidget.ss']['JUMPTOMONTH'] = 'Some Polish words';

and not:

$lang['pl_PL']['LiveCalendarWidget']['JUMPTOMONTH'] = 'Some Polish words';

Ok, works great, thanks for help and fast reaction.
I hope last problem, fragments of code LiveCalendarWidget.ss:
lines 14-16

          <% control NavigationOptions %>
            <option value="$Link" $Selected>$Month</option>
          <% end_control %>

and 28-34

			<td class="calendarDayName">$Sun</td>
			<td class="calendarDayName">$Mon</td>
			<td class="calendarDayName">$Tue</td>
			<td class="calendarDayName">$Wed</td>
			<td class="calendarDayName">$Thu</td>
			<td class="calendarDayName">$Fri</td>
			<td class="calendarDayName">$Sat</td>

names of months and days are still in English which is fine when page is displayed in English. But this is multi language page with second English language and first Polish language. How to do translations for months/days names?

How to change calendar to be displayed from Mondays not from Sundays or make it dependable from locales?

The day names are translated like this:

return strftime('%a',$timestamp);

So make sure your PHP locale is set correctly.

Yeah!
Works after setting it up like this:

		if($this->dataRecord->hasExtension('Translatable')) 
		{
			if ( ereg("^".Translatable::default_lang(), $_SERVER['HTTP_ACCEPT_LANGUAGE']) )
			{
				i18n::set_locale(Translatable::default_locale());
				setlocale(LC_ALL, Translatable::default_locale().'.utf8');
			}
			else
			{
				Translatable::set_current_locale("en_US");
				i18n::set_locale("en_US");
				setlocale(LC_ALL, "en_US.utf8");
			}
		}

How to translate 'Start' and 'End' words in $CalendarFilterForm?

You can use CalendarFilterFieldSet.START and CalendarFilterFieldSet.END. Glad it's working!

Mission accomplished:) Thanks UncleCheese for Your great help!