I know that this is a bit of a stretch, but try dialing 691 + 00 from one of the phones to see if this goes away. If it does, repeat this at all of the other phones.
Ed, I would think this could be the problem except it happens after dialing 9, not after picking up the handset or pressing speaker button. I don't think auto line select (or hot line as it is now called) could be turned on accidentally and still use the 9 button. The code to grab line 2 would have to be 6911388002 would it not? I think this is a stretch as well.