[Refer to the commentaries of: at-Tabaree, al-Qurtobee, ibn Katheer, al-Baghawee, ash-Shawkaanee, as-Samaa`aanee and as-Sa`dee].
In fact at-Tabaree quotes the following narrations:
a) Ibn Zayd said about this verse, "do not do so loudly"
b) Mujaahid said, "they have been commanded to perform His dhikr within themselves with humility"
c) Ibn Juraij said, "...it is detested to raise the voice and shout when performing supplication."
Al-Qurtobee comments on the meaning of, "without loudness in words" stating,
"Meaning such that only you can hear your words as Allaah said,
'Neither say your prayer loudly nor in a low voice but seek a middle course.' [al-Israa (17): 110].
i.e. between loudness and silence. This proves that raising ones voice is prohibited based on what has been previously discussed in a number of places."
Ibn Katheer said, "this is how it is recommended to perform dhikr - that it not be like a call nor very loud."
3) As for the saying of Allaah,
"So when you have accomplished your holy rites, celebrate the praises of Allaah, as you used to celebrate the praises of your fathers - indeed, with far more heart and soul." [al-Baqarah (2):200]
Then al-Baghawee and as-Sa`dee state that the meaning of 'aw ashadda dhikraa' is that this dhikr be performed more frequently and with more desire then their celebration of the praises of their fathers. Hence there is absolutely no proof here that one can shout or dance etc. as claimed by some innovators.
4) However on some occasions it is allowed to say some adhkaar loudly such as those that openly manifest a sign from the signs of Islaam, in which it is legislated to raise the voice at specific occasions or for specific phrases. For example the talbiyyah for Hajj and the takbeer after completing the Salaah.
It is in this way that the great Hanafee Imaam, at-Tahaawee reconciles the ahaadeeth commanding one to be silent when performing dhikr and those that say that one should say the talbiyyah for Hajj loudly in his amazing book 'Sharh Mushkil al-Aathaar' [14/491-501]
5) The hadeeth of Abu Musaa,
"We were in the company of the Prophet (SAW) on a journey, and whenever we ascended a high place, we used to say takbeer [in a loud voice]. The Prophet (SAW) said, 'O people! Be kind to yourselves for you are not calling upon One Who is deaf or absent, rather You are calling upon One Who is All-Hearing, and All-Seeing.'
Then he came to me as I was silently reciting, 'Laa hawla walaa quwwata illaa billaah.' [There is no might or motion except with Allaah]. He said, 'O Abdullah bin Qays! Say: Laa hawla walaa quwwata illaa billaah for it is one of the treasures of Paradise.'
Or he said, 'Shall I tell you a word which is one of the treasures of Paradise? It is: Laa hawla walaa quwwata illaa billaah.'"
6) The hadeeth of Abu Musaa,
"We were in the company of the Messenger of Allaah (SAW). Whenever we went up a high place we used to say the takbeer and tahleel loudly. The Prophet (SAW) said, 'O People be merciful to yourselves for you are not calling upon One who is deaf or absent. Indeed He is with you, indeed He Sees and is close.'"
Ibn Hajr al-Asqalaanee said in 'Fath al-Baaree' [6/166], "at-Tabaree said, 'this hadeeth constitutes evidence that is disliked to raise ones voice when supplicating and performing dhikr, this was the opinion of generality of the Salaf from the Sahaabah and Taabi`een.' [However] the style [of writing] of Bukhaaree dictates that this [hadeeth] specifically refers to the takbeer said [when going to and returning from] war. As for raising the voice on other occasions then it has preceded in the Book of Prayer from the hadeeth of ibn Abbaas that they used to say the dhikr loudly during the lifetime of the Prophet (SAW) after they had completed the obligatory prayers. The discussion concerning this has preceded there."
7) While discussing the hadeeth of ibn Abbaas in 'Fath' [2/414]
It seems that ibn Hajr determines that the meaning of dhikr in the hadeeth of ibn Abbaas is the takbeer as mentioned in another narration of ibn Abbaas also reported by Bukhaaree and that the first thing the Sahaabah said after completing the prayer was the takbeer.
He also quotes the saying of an-Nawawee, "ash-Shaafi`ee said concerning this dhikr after the Salaah that they said it loudly for a short time only for the purpose of teaching the mannerism of the dhikr and they did not persist in doing so. The preferred course is that the Imaam and followers say the dhikr in a low voice unless there exists the need to teach others."
Hence it would be preferred to say the takbeer loudly after the prayer and the rest of the dhikr quietly.
And in conclusion the general course for dhikr is that it be done quietly, in the way legislated by Allaah and His Messenger (SAW) and that there is no leeway in introducing new mannerisms of performing it.
Our Lord Most High knows best.