How to customize bibtex numbering in a document?

Here's a version of the solution I suggested to get you going. Given the limited use of this, it's probably not worth making the solution any more sophisticated. The basic syntax of a reference is:

\mycite{<number>}{<bib-key>}

If you want to refer to an already used citation (introduced with \mycite) you can simply use \ref{<bib=key}.

You then introduce the actual bibliography items using the \mybib for each item. These will appear with the number you used in the \mycite command, and will appear in the order in which you enter them in the itemize environment.

\begin{filecontents}{\jobname.bib}

@book{Knuth1984texbook,
    Author = {Knuth, D.E.},
    Title = {The TEXbook, volume A of Computers and typesetting},
    Year = {1984}}

@book{Chomsky1957,
    Address = {The Hague},
    Author = {Noam Chomsky},
    Publisher = {Mouton},
    Title = {Syntactic Structures},
    Year = {1957}}

@book{Chomsky1965,
    Address = {Cambridge Mass.},
    Author = {Noam Chomsky},
    Publisher = {{MIT} Press},
    Title = {Aspects of the Theory of Syntax},
    Year = {1965}}
\end{filecontents}
\documentclass[12pt]{article}
\usepackage{natbib}
\usepackage{calc}
\usepackage{etoolbox}
\usepackage{bibentry}
\usepackage{enumitem}
\SetLabelAlign{bibright}{\hss\llap{[#1]}}
\newcounter{mynum}
\newcommand\mycite[2]{[#1]\setcounter{mynum}{0}\addtocounter{mynum}{#1-1}\refstepcounter{mynum}\label{#2}}
\newcommand\mybib[1]{\item[\ref{#1}]\bibentry{#1}}

\begin{document}
\section{First section}

This document is an example of \texttt{thebibliography} environment using 
 bibliography management. Three items are cited: \emph{Syntactic Structures} 
book \mycite{6}{Chomsky1957}, \emph{Aspects} \mycite{4}{Chomsky1965}, and  
Donald Knuth's TeXBook \mycite{10}{Knuth1984texbook}. The Linguistics related items are
[\ref{Chomsky1965},\ref{Chomsky1957}].
\medskip
\bibliographystyle{unsrtnat}
\nobibliography{\jobname}
\begin{itemize}[labelwidth=!,labelsep=1em,align=bibright]
\mybib{Chomsky1957}
\mybib{Chomsky1965}
\mybib{Knuth1984texbook}
\end{itemize}
\end{document}

You can first prepare your bibliography in the usual way. Then you can set the numbers you prefer in the way shown below, by adding the code between %%START and %%END.

The filecontents environment is used just for the example, use your own database.

\begin{filecontents}{\jobname.bib}
@book{Knuth1984texbook,
    Author = {Knuth, D.E.},
    Title = {The \TeX book, volume A of Computers and typesetting},
    Publisher = {Addison-Wesley},
    Year = {1984},
}
@book{Chomsky1957,
    Address = {The Hague},
    Author = {Noam Chomsky},
    Publisher = {Mouton},
    Title = {Syntactic Structures},
    Year = {1957},
}
@book{Chomsky1965,
    Address = {Cambridge Mass.},
    Author = {Noam Chomsky},
    Publisher = {MIT Press},
    Title = {Aspects of the Theory of Syntax},
    Year = {1965},
}
\end{filecontents}

\documentclass{article}
\usepackage{xpatch} % also loads expl3

%%START
\makeatletter
\xpatchcmd{\@bibitem}
  {\item}
  {\item[\@biblabel{\changekey{#1}}]}
  {}{}
\xpatchcmd{\@bibitem}
  {\the\value{\@listctr}}
  {\changekey{#1}}
  {}{}
\makeatother

\ExplSyntaxOn
\cs_new:Npn \changekey #1
 {
  \str_case:nVF {#1} \g_changekey_list_tl { ?? }
 }
\cs_new_protected:Npn \setchangekey #1 #2
 {
  \tl_gput_right:Nn \g_changekey_list_tl { {#1}{#2} }
 }
\tl_new:N \g_changekey_list_tl
\cs_generate_variant:Nn \str_case:nnF { nV }
\ExplSyntaxOff

\setchangekey{Knuth1984texbook}{9}
\setchangekey{Chomsky1957}{3}
\setchangekey{Chomsky1965}{7}
%%END

\begin{document}
\section{First section}

This document is an example of \texttt{thebibliography} environment using 
 bibliography management. Three items are cited: \emph{Syntactic Structures} 
book \cite{Chomsky1957}, \emph{Aspects} \cite{Chomsky1965}, and  
Donald Knuth's \TeX book \cite{Knuth1984texbook}.

\bibliographystyle{plain}
\bibliography{\jobname}

\end{document}

_{I used the same data as Alan Munn just for laziness.}