Publishers such as Elsevier and SAGE provide LaTeX templates for manuscripts to be submitted to their journals. Can one post that version of the paper in our websites if the paper has been accepted to such journals? I am referring to a manuscript that only I have modified and has not been modified by the journal.
If a journal allows authors to post their pre-prints, the general rule—although it is by no means absolute—is that you may use the manuscript in the form in which it was submitted to the journal, but you cannot use the version created by the journal's production staff.
However, you should consult the specific policies of the journal to see exactly what is or is not allowed, as not all journals allow preprints.
Regarding the general question of preprints for submitted and accepted papers, I direct you to aeismail's answer. Regarding the minutiae of journal style class files, all the ones I am used to include the basic details of the licence they are supplied under in the text of the
.cls file itself. In particular Elevier's
elsarticle.cls appears to be issued under the terms of the LaTeX Project Public License, and which is fairly clear that there isn't any great land grab being made in terms of the final product.
This doesn't apply to names or images, both of which might cause copyright issues, unless the journal's instructions clearly state otherwise.