‘Eid Takbir: What Are the Different Formulas?
Question

In ‘Eid prayer for ‘Eid al-Adha, I hear people repeat Takbir (saying "Allah Akbar" in Arabic) the following phrases:
Allahu akbar, Allahu akbar, Allahu akbar, la ilaha illa-Allah, Allahu akbar, Allahu akbar, Allahu akbar, wa Lillahi’l-hamd. Allah akbar kabira, walhamdulillah kathira, subhanAllahi bukratan wa aseela, La ilaha illa-Allah wahdahu sadaqa wa‘dah wa nasara ‘abdah wa a'azza jundahu wa hazama al-ahzaba wahdah La ilaha illa-Allah wa la na'budu illa Iyyah mukhlisina lahu’l-dina wa law kariha’l-kaafirun). 
They repeat this after each prayer (from the daily 5 prayers), is that true? If wrong, what are the correct phrases to be repeated instead?
Praise be to Allah.Formula of ‘Eid Takbir (Allahu akbar, Allahu akbar, Allahu akbar la ilaha illa-Allah...)
With regard to the format of ‘Eid takbeer : “Allahu akbar, Allahu akbar, Allahu akbar la ilaha illa-Allah, wa Allahu akbar, Allah akbar, wa Lillah il-hamd (Allah is Most Great, Allah is most Great, Allah is most Great there is no god but Allah, Allah is Most great, Allah is most great, and to Allah be praise),” this is proven from Ibn Mas‘ud (may Allah be pleased with him) and others of the early generation, whether the first takbir is said twice or three times. (See al-Musannaf by Ibn Abi Shaybah, 2/165-168; Irwa al-Ghalil, 3/125)
Formula of ‘Eid Takbir (Allahu akbaru kabira wa alhamdu Lillahi kathira…)
With regard to the format of ‘Eid takbeer , “Allahu akbaru kabira wa alhamdu Lillahi kathira wa subhan Allahi bukratan wa asila… (There is no god but Allah, Allah is most Great, Allah is most Great, much praise be to Allah and glory be to Allah at the beginning and end of the day…),” Imam al-Shafi'i (may Allah have mercy on him) said: 
If he adds to that and says: “Allahu akbaru kabira wa alhamdu Lillahi kathira wa subhan Allahi bukratan wa asila, Allahu akbar wa la na‘budu illa Allah mukhlisina lahu al-dina wa law kariha al-kaafirun, la ilaha illa-Allah wahdahu, sadaqa wa‘dah wa nasara ‘abdah wa hazama al-ahzaba wahdah, la ilaha illa-Allah wa Allahu akbar (Allah is most Great, much praise be to Allah and glory be to Allah at the beginning and end of the day. Allah is most Great and we worship none but Allah, and we make our worship purely for Him (Alone) however much the disbelievers may hate that. There is no god but Allah Alone; He fulfilled His promise and granted victory to His slave and defeated the Confederates Alone. There is no God but Allah and Allah is most Great),” then he has done well. (Al-Umm, 1/241)
Abu Ishaq al-Shirazi said in al-Muhadhdhab (1/121): 
“Because the Prophet (blessings and peace of Allah be upon him) said that atop al-Safa.” 
The matter is broad in scope, because the command is to say takbir in general, and the Messenger (blessings and peace of Allah be upon him) did not single out any particular format of takbirat. Allah, may He be exalted, says (interpretation of the meaning):
“and that you must magnify Allâh [i.e. to say Takbîr (Allâhu-Akbar; Allâh is the Most Great) for having guided you.” [al-Baqarah 2:185]. 
So one may follow the Sunnah by saying any format. 
Al-San‘ani (may Allah have mercy on him) said: “In al-Sharh, there are many formats narrated from a number of imams, which indicates that the matter is broad in scope and the general wording of the verse indicates that.” (Subul al-Salam, 2/72)
Ibn Habib said: 
“The dearest to me is to say: Allahu akbar, Allahu akbar, la ilaha illa-Allah wa Allahu akbar, wa Lillahi al-hamd ‘ala ma hadana, Allahummaj'alni laka min al-shakireen (Allah is most Great, Allah is most Great, there is no god but Allah and Allah is most Great; praise be to Allah for having guided us; O Allah, make us among those who give thanks to You).
The format preferred by Yazid was: “Allahu akbaru kabira wa alhamdu Lillahi kathira wa subhan Allahi bukratan wa asila, wa la hawla wa la quwwata illa Billah (Allah is most great, much praise be to Allah and glory be to Allah at the beginning and end of the day, and there is no power and no strength except with Allah).” And he said: Whatever you add or subtract, or whatever else you say, there is nothing wrong with it.” (‘Aqd al-Jawahir al-Thaminah, 3/242)
Sahnun said: “I said to Ibn al-Qasim: Did Malik mention any particular takbir to you? He said: No. He said: Malik did not say anything specific concerning these matters.” (Al-Mudawwanah, 1/245) 
Imam Ahmad said: “It is broad in scope.”
Ibn al-‘Arabi said: Our scholars favoured the view that takbir is general in scope, which is the apparent meaning of the Quran, and I am inclined to favour this view.” (al-Jami‘ li Ahkam al-Quran, 2/307) 
Forms of ‘Eid takbir reported from the salaf
“Allahu akbar, Allahu akbar, Allahu akbar wa Lillahi al-hamd, Allahu akbar wa ajall, Allahu akbar ‘ala ma hadana (Allah is most Great, Allah is most Great, Allah is most Great and to Allah be praise; Allah is most Great and most Glorious, Allah is most Great,as He has guided us).” (Narrated by al-Bayhaqi, 3/315, from Ibn 'Abbas (may Allah be pleased with him); classed as sahih by al-Albani in Irwa al-Ghalil, 3/126)
Ibn Hajar said: “With regard to the format of the ‘Eid takbir , the most sahih that has been narrated concerning it is that which was narrated by ‘Abd al-Razzaq with a sahih isnad from Salman who said: “Proclaim Allah’s greatness: Allahu akbar, Allahu akbar, Allahu akbaru kabiran.” (Fath al-Bari, 2/462) 
Adhering to what was narrated from the Sahabah concerning that is more appropriate. 
For more, please see this answer (36442 ).
And Allah knows best.