I have read this question, but i just can not explain why exactly overfull happens in my case, so i ask for help.
First of all, two boxes in spanned cells (that ones with rotated text) produces 4 bad boxes. How can i fix it or is there workaround to suppress warnings caused by this boxes.
Minimum example
\documentclass[14pt,twoside]{extreport}
\usepackage[a4paper,
lmargin=2.5cm,rmargin=2cm,
tmargin=2.5cm,
bmargin=2cm,
marginpar=1cm,
marginparsep=0.5cm,
headheight=17pt]{geometry}
\usepackage{type1ec}
\usepackage[warn]{mathtext}
\usepackage[T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{amsmath}
\usepackage{multirow}
\usepackage{array}
\usepackage{tabu}
\usepackage{xparse}
\usepackage{pdflscape}
\NewDocumentCommand{\rot}{O{90} O{1em} m}{\makebox[#2][l]{\rotatebox{#1}{#3}}}%
\newcolumntype{Y}[1]{>{\strut\hspace{0pt}}X[#1]<{\hspace{0pt}\strut}}
\tabucolumn Y
\begin{document}
\begin{landscape}
\begin{table}[ht]
\caption{Demo table with multirow\strut}
\small
\tabcolsep=4pt
\setlength{\arrayrulewidth}{1pt}
\extrarowsep=^2pt_0pt
\begin{tabu} to \linewidth {|Y{10,C}|Y{10,C}|Y{10,C}|Y{16,C}|Y{10,C}|Y{10,C}|Y{10,C}|Y{12,C}|Y{12,C}|}\hline
\multirow{6}*[9.5ex]{%
\rot[90][7ex]{\parbox{24ex}%
{\centering First column's heading; three lines of text, six rows spanned}}}
& \multirow{6}*[9.5ex]{%
\rot[90][4.7ex]{\parbox{24ex}%
{\centering Second column's heading; two lines}}}
& \multicolumn{5}{c|}{%
\rule[-3.4ex]{0ex}{8ex}%
\parbox{0.4\linewidth}{\centering Heading of columns third to seven; single line}}
& \multicolumn{2}{c|}{%
\multirow{4}*[4.7ex]{%
\parbox{0.22\linewidth}%
{\centering Eighth and ninth column headings; %
five lines of text, two colums spanned, %
four rows spanned; and some math %
$(20\pm 5)\,^{\circ}{\rm C}$ to fill}}}\\\cline{3-7}
& & \multicolumn{5}{c|}{%
\parbox{0.4\linewidth}%
{\centering\strut At the top of the first line you can not see %
enough padding between border line and text\strut}}
& \multicolumn{2}{c|}{}\\\cline{3-7}
& & C & D & E & F & G
& \multicolumn{2}{c|}{}\\\cline{3-7}
& & \multicolumn{5}{c|}{%
\parbox{0.4\linewidth}%
{\centering\strut At the top of the first line you can not see %
enough padding between border line and text\strut}}
& \multicolumn{2}{c|}{}\\\cline{3-9}
& & C0 & D0 & E0 & F0 & G0
& \multirow{2}*{%
\parbox{\linewidth}%
{\centering multirow and multiline}}
& \multirow{2}*{%
\parbox{\linewidth}%
{\centering multirow only}}\\\cline{3-7}
& & \multicolumn{3}{c|}{Alpha}
& \multicolumn{2}{c|}{Beta}
& &\\\hline
A1 & B1 & C1 & D1 & E1 & F1 & G1 & H1 & I1\\\hline
A2 & B2 & C2 & D2 & E2 & F2 & G2 & H2 & I2\\\hline
A3 & B3 & C3 & D3 & E3 & F3 & G3 & H3 & I3\\\hline
\end{tabu}
\end{table}
\end{landscape}
\end{document}