A publisher is interested; do I nudge agents?

Are you getting an advance with this offer? If not, I wouldn't even bother agents. More than likely they won't be interested. Then again, it depends on the publisher too. Maybe if it's a mid size publisher with really good distribution. Small publishers with very little distribution, no advance, most likely no.

Regardless of whether you are being offered an advance, you need to let the agents who have requested materials know that you have interest from a publisher. Send it as a reply to any current correspondence, but change the header to OFFER RECEIVED FROM <Insert Publisher's Name>. Make sure you mention that this was a one-off thing getting your MS in front of a publisher. (You don't want to be querying publishers and agents at the same time.) If any of your outstanding queries are with agents you would really like to make an offer, you need to send them a follow-up as well. Give them a reasonable time frame in which to respond (two to three weeks).

Be prepared to receive some polite passes. Be prepared for some of them not to get back to you within that 2-3 weeks. Be prepared for some not to get back to you at all.

And best of luck.

I'm not an agent, but I don't see why you wouldn't nudge those who have partials and fulls. There's nothing rude about it. Give the agents the same info you gave here, only with the name of the editor and publishing house, and let them say yes or no. I wouldn't pre-suppose anything on your own.

I think agents who only have seen a query and haven't responded is a different issue. It's sometimes impossible for you to tell whether they haven't looked at the query yet, or they are a no-reply-means-no agent. I'd start with those who have your work in hand first. Perhaps if your dream agent hasn't responded to your query--and you're sure they aren't a no-means-no--you might follow-up there, but you'd have to do so from the slush, which makes it trickier. If you do that, put "OFFER RECEIVED-[NAME OF BOOK] in the subject line so it alerts whomever's seeing the email.

Good problem to have, though. Best of luck!

Ditto what Aggy said - and especially important to let them know the circumstances.
I failed to do that recently (whoops - total oversight on my part). The agent was understandably a bit confused and a touch grumpy because she thought I was also querying publishers at the same time. Fortunately, she asked for clarification.