Cyrillic symbols are not displayed

You're using the lmodern package, which sets the document fonts to Latin Modern, but it doesn't have support for cyrillic letters. There's Computer Modern Uncode for cyrillic and greek.

For XeLaTeX, add

\usepackage{fontspec}
\setmainfont[
  Ligatures=TeX,
  Extension=.otf,
  BoldFont=cmunbx,
  ItalicFont=cmunti,
  BoldItalicFont=cmunbi,
]{cmunrm}
\setsansfont[
  Ligatures=TeX,
  Extension=.otf,
  BoldFont=cmunsx,
  ItalicFont=cmunsi,
]{cmunss}

just before \usepackage[english,russian]{babel}, assuming that cm-unicode is installed into your TeX distribution.

For LuaLaTeX it's sufficient to add

\usepackage{fontspec}
\setmainfont{CMU Serif}[Ligatures=TeX]
\setsansfont{CMU Sans Serif}[Ligatures=TeX]

and if you want to use good old pdfLaTeX, just add the usual

\usepackage[T2A]{fontenc}
\usepackage[utf8]{inputenc}

(in all cases remove the \usepackage{lmodern} line).

Note, that for pdfLaTeX the correct fonts are selected automagically after you specify the font encoding (T2A), but for LuaLaTeX and XeLaTeX you'd have to set them explicitly which is a pity.

I've compiled with OVERLEAF. I hope I have helped you.

\documentclass{beamer}
\usepackage{lmodern}
\usepackage[english,russian]{babel}
\usepackage[T1,T2A]{fontenc}
\usepackage[utf8]{inputenc}
% Стиль презентации

\usetheme{Warsaw}
\begin{document}
\title{Все что вы хотели знать о сферическом коне в вакууме, но боялись спросить}  
\author{Олень Северный}
\institute{Научно исследовательский институт физико-матетматических проблем}
\date{Москва, 2010} 
% Создание заглавной страницы
\frame{\titlepage} 
% Автоматическая генерация содержания
\frame{\frametitle{Содержание}\tableofcontents} 
\end{document}