Check the public ODP forum (do a G search on ODP forum). My experience is that it has taken over 18 months to get listed.
It took me about 8 months, and that was only because I was eventually able to contact the editor for the category and speak with him via email.
I've seen a site added two days after submission and I've also seen sites take over a year. It's a fire-and-forget thing - set a reminder to check it once a month or so and head over to the ODP forums after 4 or 5 months...
The ODP forum will allow you to ask an editor to look into it for you. They were quick and friendly to reply to me and even suggested a second category that I could legally apply to. They recommend waiting 6 months before posting a submission status request and make sure you read the guidelines about posting as they are quite specific.
Wait one month from last suggestion before enquiring the first time.
Wait 6 months between status requests.
In general terms, it can take from a day to more than two years, mostly depending upon the category.
Spammy categories are a pain to edit, so editors tend to ignore them. Esoteric categories can be the best or the worst -- the best if there is an editor who shares the interest, the worst if none share the interest.
Contacting the editor directly usually does more harm than good. Editors are encouraged not to reply to submitters: there is a long rich history of submitters acting poorly when they don't get the answer they want.
> Wait one month from last suggestion before enquiring the first time
And if you submitted to another category within the first 30 days, start counting another 30 days before posting to the forum.
Do not resubmit. It will only may you wait longer.
On the other hand, I've seen sites added within couple of weeks to high PR categories. It was done by SEOs who claim they specialize in submitting to DMOZ.
>> It was done by SEOs who claim they specialize in submitting to DMOZ. <<
Please report the URL(s) of the sites, and/or categories involved, using the Report Abuse tool, and that will be rapidly and vigorously looked at.
I would say, the key to DMOZ submission is submitting at the right place, ONCE and with correct guidelines. I see sites with no relavance submitted in categories and that bothers you a hell lot. SPAM/Automated/SUP submissions stuffed with keywords do nothing but delay listing.