Firstly: 

There are a number of conditions which must be met for it to be permissible to translate the meanings of the names and attributes of Allah into a language other than Arabic: 

1.     The one who is translating the words should have deep knowledge of the Arabic language and of the language into which he is translating.

2.     He should be trustworthy in his translation.

3.     He should have knowledge of sharee‘ah and he should be a follower of Ahl as-Sunnah wa’l-Jamaa‘ah, otherwise he cannot be trusted not to introduce misguided and deviant beliefs into his translation. 

For a fatwa from the scholars discussing the conditions of this matter being permissible, please see the answers to questions no. 9347 and 98553 

Secondly: 

One of these rulings is swearing oaths. Oaths may be sworn by any of the names and attributes of Allah, may He be exalted, even if that is in a language other than Arabic. Whoever utters these words referring to the Lord, may He be glorified and exalted, then his oath is binding and he must offer expiation if he breaks it. 

Ibn Hazm said: There is no (valid) oath except one that is sworn by Allah, may He be glorified and exalted, either by one of His names or by one of the attributes that He has told us of, and not referring to anyone other than Him, such as the Controller of the hearts, the Inheritor of the earth and everything on it, the One in Whose hand is my soul, the Lord of the Worlds, and so on. That may be said in all languages. Or (one may swear) by the knowledge of Allah, or by His power, His might, His majesty, and so on, as mentioned in the text. If a person swears by any of that, he has indeed sworn an oath and if he breaks it then he must offer expiation.

End quote from al-Muhalla, 8/30 

Ibn al-Humaam al-Hanafi (may Allah have mercy on him) said: If he says in Farsi “I swear by God”, this is an oath by Allah.

End quote from Fath al-Qadeer, 5/76 

Whatever the case, whoever refers by these words to the Lord of the Worlds, then the shar‘i rulings (on oaths) come into effect. If a person swears an oath in his own language referring to the One Lord, then the oath is binding. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: The Lord, may He be glorified, may be referred to in Arabic as Allah, ar-Rahmaan (the Most Gracious), ar-Raheem (the Most Merciful), and in Farsi as Khoda and so on, but He, may He be glorified, is One, and there are many ways to refer to Him.

End quote from al-Fataawa al-Kubra, 6/568 

But what the Muslim should use in his worship, his du‘aa’ (supplication) and all other circumstances when referring to Allah, may He be exalted and glorified, is the word “Allah” as it is, because that has become a symbol for the Muslims and something that distinguishes them, and it helps to avoid any confusion between what they mean and what others mean when they say “God”, as others may sometimes be referring to Allah, but sometimes they may be referring to something else. 

Everything that we have mentioned above applies to one who does not have a good knowledge of Arabic; as for the one who has a good knowledge of Arabic, it is permissible for him to use the translated words in order to explain Islam and help others to understand it. But when offering du‘aa’ or swearing oaths, he has to avoid doing that with words other than the known Arabic words for the divine names and attributes, as they are confirmed in the Qur’aan and Sunnah. 

And Allah knows best.