I want to know how many sunnah and nafl rak'ats one should offer in Jumuah prayer/salah according to all the 4 Imaams?
It would be great if you could tell me in details about all 4 Imaams.
Evidences for sunnah or nafl before the jumu'ah prayer
Let's start by some evidences:
"Whoever takes a bath on Friday, purifies himself as much as he can, then uses his (hair) oil or perfumes himself with the scent of his house, then proceeds (for the Jumua prayer) and does not separate two persons sitting together (in the mosque), then prays as much as (Allah has) written for him and then remains silent while the Imam is delivering the Khutba, his sins in-between the present and the last Friday would be forgiven."
(sahih al-Bukhari, also in musnad Ahmad on the authority of abu ad-Darda' and on the authority of abu Ayyub al-Ansari with different wordings)
This hadith shows that one should pray as much sets of sunnah or nafl prayers as possible once reaching the mosque on Friday until the Imam comes out for the sermon. This view is also present in this narration quoting what people used to do at the time of 'Omar ibn al-Khatab.
Note that the second narration from musnad Ahmad on the authority of abu Ayyub al-Ansari suggests that not praying is a sunnah or nafl is also an option (فيركع إن بدا) (meaning and prostrates if he wants to)!
“The Prophet (ﷺ) used to perform four Rak’ah before Friday (prayer), and he did not separate any of them.” (Sunan ibn Majah)
This hadith is even suggesting to pray a set of 4 raka'a... note that scholars consider many of the narrators in the chain as not trustworthy!
‘Did you perform two Rak’ah before you came?’ He said: ‘No.’ He said: ‘Then perform two Rak’ah, but make them brief.’” (Sunan ibn Majah)
This hadith is suggesting to pray (at least) two raka'a these two rak'a are considered something different than tahiyyat al-Masjid (the so called the salutation or greeting of the mosque) by all scholars, some interpreted them to be prayed before going to mosque, al-Majd ibn Taymiyyah (the grand father of the famous ibn Taymiyyah) has interpreted it as a sunnah before jumu'ah not including tahiyyat al-Masjid. There's also a hint of doubt that some narrators have changed the narration from "before you sit down" to "before you came", as the last has been narrated in the two sahihs on the authority of Jabir (sahih al-Bukhari, sahih Muslim) without quoting an amount (as if it was known). Note that this hadith also seems to have weaknesses!
From all of this we may conclude that there is no precise or prescribed amount quoted for sunnah or nafl before jumu'ah, but if one has time one should at least pray two raka'a if we consider the last hadith authentic (beside thaiyyat al-Masjid).
So if your question was is there what is called a sunnah ratiba before jumuah (a sunnah connected to juma'ah prayer which is performed before) then the answer is no, but you are (strongly) recommended to pray nafl if you arrive at the mosque before (and until) the Imam comes out for the sermon!
The opinion of the four madhhabs
However the hanafi, shafi'i and one view of the hanbali school of fiqh say there's a sunnah ratiba (before the jumua'h prayer) and it's amount is 2 (as a minimum, which is the view of the shafi'is and some hanbalis beside one opinion of imam Ahmad himself) and 4 rak'a (as the optimum, this the view of some hanbalis and the hanafis).
While the maliki school and the 2nd opinion in the hanbali school say there's no such a sunnah ratiba before the jumua'h prayer.
Evidences for sunnah or nafl after the jumu'ah prayer
There are evidences for two rak'a after jumu'ah:
Allah's Messenger (ﷺ) used to pray two rak'at before the Zuhr prayer and two rak'at after it. He also used to pray two rak'at after the Maghrib prayer in his house, and two rak'at after the #Isha' prayer. He never prayed after Jumua prayer till he departed (from the Mosque), and then he would pray two ra'`at at home. (see for example in sahih al-Bukhari)
according this the sunnah al-ba'diya (the sunnah after jumu'ah prayer) has to be done as two rak'a and at home not in the mosque!
There are evidences for four raka'a:
When any one of you observes the Jumu'a prayer (two obligatory rak'ahs in congregation), he should observe four (rak'ahs) afterwards. (see for example in sahih Muslim)
In his version of the hadith at-Tirmdihi he discussed this issue to some extent, he also quoted what was narrated on the authority of ibn Masu'd () who used to pray four raka'a before jumu'ah and four after the prayer (this view was considerd by ibn al-Mubarak and sufyan a-Thawri). While it was narrated that Ali ibn Abi Talib () used to order to pray first two raka'a and then four raka'a after jumuah. Ishaq and later ibn Taymiyyah said: If he prayed in the mosque he should pray four raka'a and when he prays at home two.
Imam Malik, a-Shafi'i and Ahmad preferred praying the sunnah at home based on the hadith sayng:
"... for the best prayer of a person is what is performed at his home except the compulsory congregational) prayer." (see for example sahih al-Bukhari)
View of the madhhabs
Imam Ahmad opinion is that one is free to chose whether one prays 2 raka'a or four raka'a.
The shafi'i say one may pray at least two raka'a after it but praying four would be better!
The hanafis according as-Sarakhsi in his mabsot consider praying four raka'a (without interruption by taslim) as sunnah however praying six raka'a is also considered in the madhab as you may read in the answer of a relevant post!
Tha malikis say it is makroh to pray sunnah or nafl after the tasleem of jumu'ah, but one shall pray the sunnah at home or wait until people have left the mosque (so if he prayed at home one have to pray two raka'a) and in the mosque it is strongly makrooh to pray at the place one was praying jumua'h (it was narrated that ibn 'Omar moved a person doing this, a reason for that is to let laymen clearly distinguish between 4 raka'at of dhohr and the 2 jumu'ah+2 of sunnah, as jumua'ah is totally diffetent than dhohr) and one also follows the hadith of ibn 'Omar praying two raka'a, anything more would be nafl! Note that the malikis strongly disliked it if the imam of jumu'ah prayed the sunnah at the mosque!