Imagine a fly buzzing in your ear.
It is annoying.
Now imagine you are sitting in your room trying to read, and something is bothering you.
After some time, you notice your neighbor's stereo is on, and you realize the bass vibrations were bothering you.
It was vaguely annoying, but you couldn't pinpoint it.
Now imagine a speaker who is telling you all about how to fix your life.
Some of what they say makes sense.
Some of what they say is good advice.
Some of what they say is helpful.
But for some reason, you find them annoying, and you aren't quite certain why.
They are vaguely annoying.
ell.stackexchange.com/users/3175/michelle
"Vaguely annoying": annoying but only just noticeably so.
"
In a [x] kind of way": In a similar manner to [x].
"Over-enthusiastic": enthusiastic to the point that it becomes annoying. "Motivational speaker": someone who gives lectures about how to motivate yourself.
So they are comparing the the way the dancer talks to that of an over-enthusiastic motivational speaker.
ell.stackexchange.com/users/23/Matt Ellen
"Vaguely annoying" would be understood to mean "annoying, but you cannot say exactly what qualities of the thing are irritating you".
Something about it rubs you the wrong way.
See 2b here: http://www.merriam-webster.com/dictionary/vaguely
ell.stackexchange.com/users/10264/Tᴚoɯɐuo
The sentence in concern has too many adjectives and that might have confused you.
Starting dancing this way could be vague and he invited everyone to join,
that's even strange.
But try to group those adjectives and the sentence might look better.
Okay, that’s [vaguely annoying] in an [over-enthusiatic motivational speaker]
kind of way, but...
Let's not judge
the event
but what it means is the dancing and invitation both was done in a way some over-enthusiastic motivational speaker would do.
Not exact
but this could be something like... You dance in an MJ way.
means you dance the way MJ danced.
Said that, this is vaguely annoying.
How?
In a way some over-enthusiastic motivational speaker would speak.
Edit after OP's comment: Here, vaguely means slightly.
It was a bit strange and so slightly annoying that he was about to dance that way by inviting people.
ell.stackexchange.com/users/3187/Maulik V
It basically means that the person was annoying, but there was nothing specifically annoying about them.
Their character was generally annoying.
This is described as being a bit like a motivational speaker, who tend to be overly positive, hyperactive and use too many buzzwords etc.
These habits are tolerable when a person has one or two, but the whole package is often abrasive.
You can easily infer from the choice of words, "vaguely annoying", that it was still pretty minor.
People who're seriously upset, know exactly what they're upset about.
ell.stackexchange.com/users/2057/Carl Smith
Context is ( source ):   Okay, that’s vaguely annoying in an over-enthusiatic motivational  speaker kind of way, but I’ll permit it – because what this turns into  is genuinely so joyful.   Could you explain to me, what phrase   ...vaguely annoying in an over-enthusiatic motivational speaker kind of way...   mean?  Update.  It seems I don't understand what  vaguely annoying  means...
Could you explain phrase "vaguely annoying in an over-enthusiatic motivational speaker kind of way"
ell.stackexchange.com
<meaning-in-context><phrase-meaning>
ell.stackexchange.com/questions/37859
ell.stackexchange.com/users/5754/Denis Kulagin
"Vaguely annoying" would be understood to mean annoying, but you cannot say exactly what qualities are irritating you. The person might have been annoying, but there was nothing specifically annoying about them. This is described as being a bit like a motivational speaker, who tend to be overly positive, hyperactive and use too many buzzwords, etc. Vaguely annoying means annoying for reasons you cannot pinpoint. It may be about over-enthusiasm.
Vaguely annoying means annoying for reasons you cannot pinpoint. It may be about over-enthusiasm.