I'm polyamorous too and, well, this is sort of new for me too (at least in practice) but learning from others I found suitable ways to act.
I've seen that most answers seem to be a little tone deaf on the importance of not making the 3rd partner feel out of place or disrespected.
The alleviation strategy is one of my favorites to address someone who's judgement influence in your lives is unpredictable, which is almost anyone.
Being open about it is great, bravery is appreciated.
I don't think you want people to focus on that too long though, after you introduced your companions, change the topic of conversation to something your audience feels comfortable with. Your audience can be a single person or a group. Steer the conversation to something they know about, something where they don't feel like stepping on cracked unstable ground.
That's the simplest way to maintain the conversation going, a nice friendly social interaction.
This strategy is necessary when the person addressed is someone who's judgement has an influence on your lives; could be your business partners, your parents, and so on, people with some authority or at least high credibility on your circles.
Prepare something cool and positive to say about your polyamorous relationship, something positive that doesn't cause contrast with your audience's situation. Something neutral like:
Having them in my life is great
You want to avoid anything that brings competition or comparisons with their own lifestyle. This way you are conveying there's nothing to be concerned about, plus, you established both have respect and appreciation from you and it is the best way to induce your audience to respond likewise. But you don't want to get stuck there, follow that by saying something nice about each one of the people you are introducing, not necessarily relating your comment to the relationship, it is better to remind them how they are more similar to your audience rather than different.
'X' works in the same field as you...
'Y' was just talking about that movie you recommended me...
And then make the conversation about that, closer to something your audience feels comfortable with, steering towards the alleviation strategy that I mentioned first. Like a failsafe protocol.
A measure to prevent these awkward situations is not only to be open about it but also public, in advance.
The more people in your social circles are informed in advance of your polyamorous status, the least likely the situation you encountered will happen, because when people are approaching the three of you they will process all the possibilities on their minds before making contact.
- Be sure to inform the most respectful friends first before going public and let them know that it isn't a secret, they will help you to understand the main concerns of people who don't understand in a respectful way.
- Tell your family and your closest friends first so you are in a position to set the narrative and be on the steering wheel.
- Going public, don't be afraid to tell gossipy individuals in your circles, the more people know the better.
- Be sure to attend parties and public events alone and with your partner soon after making your polyamorous status public, this way people will have the information fresher on their mind when they see you and they'll start with the mental guesswork without disturbing you. Some might offer comments on your public status, that's cool, there's no other person present to feel awkward.
Nice people will make an effort to dissimulate their own awkwardness and will focus on normal conversation, curious people with a lesser sense of tact will ask things because they had never before encountered the ongoing scenario where they had the chance to ask about this real life situation (even if their timing is not adequate).
My experience with all of this was to start by writing on my personal blog and calling my mother and having a conversation with her to prevent her from being weird with my bisexual girlfriend, and I was very clear:
you will have to get used to see me with more than one girl and treat them with the same respect you treat me
The conversation was a bit more broad and tactful as you might expect but that was the main idea to get across. I also made sure she understood:
this is what makes me happy and it makes my partners happy, it is an agreement and no one is suffering, no one is being taken advantage of or anything like that, all the opposite, we are even more happy, the three of us together
It helped explaining how on contrast other relationships had made me unhappy or even miserable because bisexuality isn't uncommon at all and more than a couple previous girlfriends had been bisexual, which lead to unnecessary drama and neither party had dared to propose trying the polyamorous way to include one or two lovers in our lives and for them to include us likewise. I personally prefer someone stable though, and my girlfriend does too, that contributes to both our happiness and satisfaction. Mom remembered how miserable I was during the time of one of those relationships I mentioned and now that she understood why and that she understood I didn't want to be fooling around, she became if not encouraging, at least sympathetic and supportive (which was surprising because she's a conservative and religious person, it's hard to go against happiness).
Everyone in my circles is already gossiping about it and their conversation shows they are sort of avoiding to talk about it but already prepared for the situation.
This doesn't mean it won't ever ever happen, I know there are people with things they can't keep to their own, for whatever reason, curiosity or disapproval, I'm prepared to address their concerns, but timing is much more important as you have already noticed. An "avoiding to talk about it" attitude as the first impulse is exactly what you want, to avoid the awkward explanations during an inappropriate time. They will be able to approach you at a better time if they so desire.
Best of luck.