How to remove the indent after enumerate

The culprit is the \IEEEPARstart. Despite what the style file says this has not been fixed to allow direct inclusion of environments in the initial paragraph. To work around this you can just make sure there is a \par before your enumerate. Here is the same text first time without \par, second time with:

\documentclass[journal]{IEEEtran}

\begin{document}

\section{Introduction}
\IEEEPARstart{T}{he} Lorem ipsum dolor sit amet, consectetuer
adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet
dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis
nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex
ea commodo consequat. Mirum est notare quam littera gothica, quam nunc
putamus parum claram, anteposuerit litterarum formas humanitatis per
seacula quarta decima et quinta decima. Eodem modo typi, qui nunc
nobis videntur parum clari, fiant sollemnes in futurum:
\begin{enumerate}
\item Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed
  diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam
  erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci
  tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo
  consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate
  velit esse molestie consequat, vel illum dolore eu feugiat nulla fa.
\item Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed
  diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam
  erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci
  tation ullamcorper suscipit lobortis nisl.
\end{enumerate}
The rest of the paper is organized as follows. Section II provides an
introduction to Lorem ipsum dolor sit amet, consectetuer adipiscing
elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna
aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud
exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea
commodo consequat. Duis autem vel eum iriure dolor in hendrerit in
vulputate velit esse molestie consequat.

\section{Introduction}
\IEEEPARstart{T}{he} Lorem ipsum dolor sit amet, consectetuer
adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet
dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis
nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex
ea commodo consequat. Mirum est notare quam littera gothica, quam nunc
putamus parum claram, anteposuerit litterarum formas humanitatis per
seacula quarta decima et quinta decima. Eodem modo typi, qui nunc
nobis videntur parum clari, fiant sollemnes in futurum:\par
\begin{enumerate}
\item Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed
  diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam
  erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci
  tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo
  consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate
  velit esse molestie consequat, vel illum dolore eu feugiat nulla fa.
\item Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed
  diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam
  erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci
  tation ullamcorper suscipit lobortis nisl.
\end{enumerate}
The rest of the paper is organized as follows. Section II provides an
introduction to Lorem ipsum dolor sit amet, consectetuer adipiscing
elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna
aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud
exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea
commodo consequat. Duis autem vel eum iriure dolor in hendrerit in
vulputate velit esse molestie consequat.

\end{document}

I think this is a bug in IEEEtran.cls in the macro \IEEEPARstart. You can get around it by putting a blank line after \end{enumerate} and putting \noindent at the start of the following paragraph.

The problem comes down to the two parameters \hangindent and \hangafter. These are given values that allow the large T to fit into the two-line indentation in the first paragraph. These values must persist until the end of the paragraph, because only when the full paragraph is collected does TeX break it into lines using these values to get the lengths of the first two lines.

These values are reset to zero at the end of the paragraph, more specifically, at the first invocation of the TeX "end-of-paragraph" primitive. Unfortunately, in this example, that happens inside a group and the reset values are lost. Thus, the paragraph that follows has those same values and you get the same two lines of indentation as were used earlier to place that large T.

Another workaround is to put the following right after \end{enumerate}:

\makeatletter \@@par \makeatother

This invokes the primitive end-of-paragraph but not \par itself, so that the values of \hangindent and \hangafter are restored to 0, but the magic that keeps the next line from indenting remains in effect.