>what shall I do
In relation to DMOZ: nothing.
Not related to DMOZ: that is only for you to decide.
>do i have to resubmit my site?
No. The fact that a category is updated does not mean that all sites suggested to that category are reviewed. Several things could have happened to your site
* it is still waiting review
* it was send to a better category
* it was rejected
In none of these 3 cases is it needed to suggest the site again.
>what procedure to follow?
There is no procedure other than to suggest your site (and you already did so)

23 August was only a week ago, zaneta. Even if I was paying a directory for inclusion, I don't think I'd expect a turnaround within one week; but certainly a request for a free link isn't going to be fulfilled that quickly more than once in a blue moon.

I know that it frustrates some webmasters to hear me say this, but the "site suggestion" mechanism at the ODP is not our highest priority. Only about 1/3 of the sites I add to the directory ever come from the pool of suggested sites. The rest are URLs that I came across, well, pretty much the same way all the sites' other users do: by following a link to it, by finding it in a search engine or another directory, by seeing an ad for it, by interacting with a real-life company or organization and wondering if they have a website and going to look for it, by getting email from a friend to check out this interesting website, by random serendipity.

If you've suggested a site to a small category that seems to be stalled--say, a category on Elbonian arts and crafts that has only eight sites listed in it and hasn't been updated in a year--feel free to send me a stickymail with the URL of the category in question and I'll take a look at it (the whole category, that is to say, not your site in particular.) Occasionally it's the case that an obscure topic gets neglected just because no volunteer happens to be interested in it, and that's an issue I'm happy to do what I can to address.

But if you've submitted a site to a huge commercial category with 175 sites already listed in it that gets updated every couple of months, there's probably just a huge backlog of site submissions in that category (many of which are spam) and the editors are finding most of their sites to list from another source. There's nothing that can be done about that other than raising your site's visibility (which is coincidentally good for your site in lots of other ways, so it's a productive tack to take.)

Submit once, to one category.

The "last edit" date shows that "something" happened in that category on one or more entries.

It does not mean that all sites were reviewed.