LaTeX.org

If you switch to biblatex, you can specify this for any style with the option

sorting=none

You might also want to look at the biber backed to biblatex - as of version 0.9.4 it can suppress arbitrary fields in your data source, not just DOI etc. It can also re-map fields and entrytypes to others.

You don't have to use biber but it's highly recommended. But best be clear. You have two options:

Use bibtex and a bibtex style like natbib
Use biblatex which utilises a backend processor of which there are two:

bibtex - biblatex uses this just for sorting and labelling, not for styling ...

Don't forget that the problem with Unicode and bibtex isn't really that it mangles it often. You can usually get round it using some macro like \greektext{} or character macros in general but this only "solves" part of the problem because then the sorting of your bibliography is completely broken ...

As an addendum, note that cl-bibtex (and I don't think bibtexu, a recent Unicode bibtex) doesn't really sort with full Unicode support like biber. Real Unicode sorting needs CLDR support for many common locales. One of the main problems with Unicode support is sorting of bib entries, not just not ...

Biber cannot work as a stand-alone bibtex replacement - it is tied closely to biblatex. I would strongly consider switching to biblatex anyway - it's a lot more flexible than plain bibtex.