Although you can do this with a wrapfigure or simply two minipages, for a document with several margin figures, this is the normal look & fell for the peculiar but elegant tufte-hadout or tufte-book class, as they left a wide right margin to provide room for figures, tables or sidenotes.
For images, simply use the marginfigure instead of the figure environment. Note that you can adjust the vertical position of the figures and put text than extent to the right margin, making fake wrappings.
If you do not want the style of tufte classes in another aspects (not justified text, not numbered sections, etc.), at some extent they can be easily tuned to look more like standard classes, so give them a try. An example resembling a bit some standard class:

\documentclass[justified,twoside]{tufte-handout}
\title{A Minimal Working Example}
\usepackage{lipsum,blindtext}
\usepackage{graphicx}
\setcounter{secnumdepth}{1}
\setcaptionfont{\sffamily}
\titleformat{\section}{\bfseries\Large}{\thesection}{1em}{}[]
\begin{document}
\section{Research}
\lipsum[1]
\begin{marginfigure}[-25em]
\includegraphics[width=\textwidth]{example-image}
\caption{A tiny caption.}
\end{marginfigure}
\lipsum[2]
\begin{marginfigure}[-18em]
\includegraphics[width=\textwidth]{example-image-a}
\caption{The nice image A.}
\end{marginfigure}
\begin{fullwidth}
\lipsum[3]
\end{fullwidth}
\end{document}
Edit: To make like asked in the edited question, here are another ways:

\documentclass{article}
\usepackage[margin=2cm]{geometry}
\usepackage{wrapfig}
\usepackage{lipsum}
\usepackage{graphicx}
\usepackage{adjustbox}
\def\parimg#1#2#3{\noindent%
\adjustbox{valign=t}{\begin{minipage}[c]{\dimexpr.95\linewidth-.#3\linewidth}#1\end{minipage}}\hfill%
\adjustbox{valign=t}{\begin{minipage}[c]{.#3\linewidth}\includegraphics[width=\linewidth]{#2}\end{minipage}}\par}
\parskip2em plus 1em minus 1em
\begin{document}
\begin{wrapfigure}[6]{r}[0pt]{3cm}
\includegraphics[width=\linewidth]{example-image-a}
\end{wrapfigure}
\lipsum[1]
\lipsum[2]
\parimg{\lipsum[3]}{example-image-b}{4}
\parimg{\lipsum[4]}{example-image-c}{3}
\lipsum[5]
\end{document}
wrapfigureenvironment. It works fine as long as there's no list environment near it. – Bernard Feb 12 '17 at 16:49enumitem) and the plain TeX macro packageinsbox. – Bernard Feb 13 '17 at 12:53