You can pass explicit option to titlesec and specify the title as #1. The following may serve as the launch pad for your further refining and improvements.
\documentclass[a4paper,twoside]{article}
\usepackage[svgnames,x11names]{xcolor}
\usepackage{tikz}
\usetikzlibrary{fadings,patterns,backgrounds,fit}
\usepackage{titletoc}
\usepackage[toctitles,pagestyles,explicit]{titlesec}
\usepackage{multicol}
\oddsidemargin=-10.4mm
\evensidemargin=-20.4mm
\topmargin=-22mm
\textwidth=190mm
\textheight=275mm
\headheight = 5mm
\headsep = 2mm
\footskip = 7mm
\titleformat{\part}[block]{}{}{1ex}%
{\begin{tikzpicture}[baseline={([yshift=-.6ex]current bounding box.center)}]
%\fill [Gold2,path fading=north] (0,-1) rectangle (\columnwidth,1.5);
\node[fill=DarkGoldenrod1,rectangle,rounded corners,text=white,anchor=west,font=\huge\bfseries\sffamily] (a) at (0,0) {Part
\thepart};
\node[fill=none,text width= 0.7\columnwidth,text=red,anchor=north west,align=left,font=\huge\bfseries\sffamily] (b) at (a.north east) {#1};
\begin{scope}[on background layer]
\node[fill=Gold2,path fading=north] [fit = (a)(b)] (B) {};
\node[pattern=vertical lines,pattern color=blue!50,path fading=north] [fit = (a)(b)] (A) {};
\end{scope}
\end{tikzpicture}%
}
[]
\begin{document}
\part{The trends in art in XX}
\newpage\twocolumn
\part{The World Wars influence}
\newpage\onecolumn
\begin{multicols}{2}
\part{The IT influence}
\end{multicols}
\end{document}

Without explicit option, you can do it like this (thanks to egreg)
First define
\newcommand{\mypart}[1]{%
\begin{tikzpicture}[baseline={([yshift=-.6ex]current bounding box.center)}]
\node[fill=DarkGoldenrod1,rectangle,rounded corners,text=white,anchor=west,font=\huge\bfseries\sffamily] (a) at (0,0) {Part
\thepart};
\node[fill=none,text width= 0.7\columnwidth,text=red,anchor=north west,align=left,font=\huge\bfseries\sffamily] (b) at (a.north east) {#1};
\begin{scope}[on background layer]
\node[fill=Gold2,path fading=north] [fit = (a)(b)] (B) {};
\node[pattern=vertical lines,pattern color=blue!50,path fading=north] [fit = (a)(b)] (A) {};
\end{scope}
\end{tikzpicture}%
}
Then declare the \titleformat like
\titleformat{\part}[block]{}{}{1ex}%
{\mypart}
[]
Full code again:
\documentclass[a4paper,twoside]{article}
\usepackage[svgnames,x11names]{xcolor}
\usepackage{tikz}
\usetikzlibrary{fadings,patterns,backgrounds,fit}
\usepackage{titletoc}
\usepackage[toctitles,pagestyles]{titlesec}
\usepackage{multicol}
\oddsidemargin=-10.4mm
\evensidemargin=-20.4mm
\topmargin=-22mm
\textwidth=190mm
\textheight=275mm
\headheight = 5mm
\headsep = 2mm
\footskip = 7mm
\newcommand{\mypart}[1]{%
\begin{tikzpicture}[baseline={([yshift=-.6ex]current bounding box.center)}]
\node[fill=DarkGoldenrod1,rectangle,rounded corners,text=white,anchor=west,font=\huge\bfseries\sffamily] (a) at (0,0) {Part
\thepart};
\node[fill=none,text width= 0.7\columnwidth,text=red,anchor=north west,align=left,font=\huge\bfseries\sffamily] (b) at (a.north east) {#1};
\begin{scope}[on background layer]
\node[fill=Gold2,path fading=north] [fit = (a)(b)] (B) {};
\node[pattern=vertical lines,pattern color=blue!50,path fading=north] [fit = (a)(b)] (A) {};
\end{scope}
\end{tikzpicture}%
}
\titleformat{\part}[block]{}{}{1ex}%
{\mypart}
[]
\begin{document}
\part{The trends in art in XX}
\newpage\twocolumn
\part{The World Wars influence}
\newpage\onecolumn
\begin{multicols}{2}
\part{The IT influence}
\end{multicols}
\end{document}
If you want to change the height of the rectangle, play with ,minimum height=2cm,yshift=0.5cm in
\begin{scope}[on background layer]
\node[fill=Gold2,path fading=north,minimum height=2cm,yshift=0.5cm] [fit = (a)(b)] (B) {};
\node[pattern=vertical lines,pattern color=blue!50,path fading=north,minimum height=2cm,yshift=0.5cm] [fit = (a)(b)] (A) {};
\end{scope}

pgfonlayerin the TikZ/PGF reference manual. – yo' Oct 16 '14 at 12:35