The parameters in the font metric file for the Alegreya font are wrong; the x-height (stored in \fontdimen5) is too small as the following test file shows. Some accents are placed correctly, because in the T1 encoding they're precomposed; the problem shows only when the accented letter is not precomposed and TeX's method (based on \fontdimen5) must be used.
\documentclass{scrbook}
\usepackage[T1]{fontenc}
\usepackage{Alegreya}
\begin{document}
The x-height: \expandafter\texttt\expandafter{\the\fontdimen5\font}
The height of `x': \expandafter\texttt\expandafter{\the\fontcharht\font`x}
\fontdimen5\font=\fontcharht\font`x
Rodion \^{S}edrin
\u{U}ladz\`{i}m\`{i}r Damarackij
V\^{a}\v{c}\`{e}sla\u{u} Kuzn\^{a}co\u{u}
\end{document}
(the \expandafter tokens are just for pretty printing the value of the parameter using the current font before \texttt changes it).

In the test file I change the x-height to a more sensible value and you can see that the result is correct.
You should file a bug report. For the moment you can work around the issue with the following hack:
\documentclass{scrbook}
\usepackage[T1]{fontenc}
%%%%% ADD THIS TO YOUR PREAMBLE BEFORE LOADING Alegreya
\DeclareFontFamily{T1}{Alegreya-LF}{}
\newcommand{\adjustalegreya}{\fontdimen5\font=\fontcharht\font`x }
\makeatletter
\let\Alegreya@@scale\@empty
%%% uncomment the next line if you want to scale the font,
%%% changing the value to what suits you
% \def\Alegreya@@scale{s*[0.9]}%
\makeatother
\DeclareFontShape{T1}{Alegreya-LF}{k}{n}{
<-> \Alegreya@@scale Alegreya-Black-lf-t1
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{k}{it}{
<-> \Alegreya@@scale Alegreya-BlackItalic-lf-t1
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{k}{sl}{
<-> ssub * Alegreya-LF/k/it
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{b}{n}{
<-> \Alegreya@@scale Alegreya-Bold-lf-t1
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{b}{it}{
<-> \Alegreya@@scale Alegreya-BoldItalic-lf-t1
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{b}{sl}{
<-> ssub * Alegreya-LF/b/it
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{m}{n}{
<-> \Alegreya@@scale Alegreya-Regular-lf-t1
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{m}{it}{
<-> \Alegreya@@scale Alegreya-Italic-lf-t1
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{m}{sl}{
<-> ssub * Alegreya-LF/m/it
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{bx}{sl}{
<-> ssub * Alegreya-LF/b/sl
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{bx}{n}{
<-> ssub * Alegreya-LF/b/n
}{\adjustalegreya}
\DeclareFontShape{T1}{Alegreya-LF}{bx}{it}{
<-> ssub * Alegreya-LF/b/it
}{\adjustalegreya}
%%%% NOW YOU CAN SAFELY LOAD Alegreya (don't pass a scale option)
\usepackage{Alegreya}
\begin{document}
The x-height: \expandafter\texttt\expandafter{\the\fontdimen5\font}
The height of `x': \expandafter\texttt\expandafter{\the\fontcharht\font`x}
Rodion \^{S}edrin
\u{U}ladz\`{i}m\`{i}r Damarackij
V\^{a}\v{c}\`{e}sla\u{u} Kuzn\^{a}co\u{u}
\footnotesize
The x-height: \expandafter\texttt\expandafter{\the\fontdimen5\font}
The height of `x': \expandafter\texttt\expandafter{\the\fontcharht\font`x}
Rodion \^{S}edrin
\u{U}ladz\`{i}m\`{i}r Damarackij
V\^{a}\v{c}\`{e}sla\u{u} Kuzn\^{a}co\u{u}
\end{document}

Update
The version of Alegreya released on 2014-05-18 seems to have solved the problem. Here's the original test, without any addition except for repeating the same text in the four main styles.

\emphcommands to behave as expected for another bug. – egreg May 17 '14 at 22:44