Here I place such a construct in a \Longunderstack using my macro \thread, which is passed the total number of threads as the first argument, the color as the second argument, and the thread content as the final argument. The width of the thread stack is defined by the \def of \threadwidth. Being a stack, it cannot cross page boundaries.
I had to raise the stack 7pt to align it with the current baseline, which occurs from the borders of the \parbox I think.
\documentclass{article}
\usepackage[usestackEOL]{stackengine}
\usepackage{xcolor}
\def\stacktype{L}
\def\stackalignment{l}
\def\threadwidth{2in}
\newcommand\thread[3]{\parbox[t]{\threadwidth}{\baselineskip=#1\baselineskip\color{#2}#3}}
\begin{document}
baseline
\raisebox{7pt}{\Longunderstack{%
\thread{3}{red}{This is a test of a red paragraph which wraps every
3 lines... if we are lucky}\\
\thread{3}{blue}{\bfseries And here we have a test in which the second paragraph
is a nice dark blue.}\\
\thread{3}{cyan}{\itshape And finally, we have a test in which the third and
last paragraph is cyan.}%
}}
\end{document}

Placing it in a tabular is only complicated by the fact that the value of \baselineskip evaporates inside a tabular and so it must be saved in advance:
\documentclass{article}
\usepackage[usestackEOL]{stackengine}
\usepackage{xcolor}
\def\stacktype{L}
\def\stackalignment{l}
\def\threadwidth{2in}
\edef\tmp{\the\baselineskip}
\setstackgap{L}{\tmp}
\newcommand\thread[3]{\parbox[t]{\threadwidth}{\baselineskip=#1\baselineskip\color{#2}#3}}
\begin{document}
\begin{tabular}{|c|l|l|}
\hline
baseline &
\raisebox{7pt}{\Longunderstack{%
\thread{3}{red}{This is a test of a red paragraph which wraps every
3 lines... if we are lucky}\\
\thread{3}{blue}{\bfseries And here we have a test in which the second paragraph
is a nice dark blue.}\\
\thread{3}{cyan}{\itshape And finally, we have a test in which the third and
last paragraph is cyan.}%
}}&
\raisebox{7pt}{\Longunderstack{%
\thread{2}{orange}{If a macro breaks in the CPU and no one is there to hear it,
did it indeed break?}\\
\thread{2}{black}{I think that I shall never see, \LaTeX{} as beautiful as thee}
}}
\tabularnewline
\hline
\end{tabular}
\end{document}
