Allah swears by whatever He wills, but we can only swear by Allah and nothing else. Swearing is like glorifying, and it is not right to glorify anything or anyone other than Allah.
The Prophet ﷺ said: “Whoever has to take an oath should swear by Allah or remain silent (i.e. he should not swear by other than Allah).” [Bukhari]
The meaning of Wallahi, Billahi and Tallahi: The three words have different meanings depending on their context in speech. They may be said and mean swearing by Allah, because the Arabic letters Waw, Ba’a and Ta’a are used for swearing, so if a person says Wallahi, Billahi, or Tallahi, it means that he swears by Allah or makes an oath by Allah. On the other hand, if the word “Allah” is preceded by the letter Waw or Ba’a, then it could mean other than swearing. For example, if someone says “Ista’antu Billah,” i.e. I seek help from Allah, then the letter Ba’a here is for seeking help. Likewise, the letter Waw could mean Ist’inaf, i.e. to indicate beginning a new sentence to make a different point; like the saying of Allah “Wallahu Rau’ufum Bil Ibad” (And Allah is Kind to His servants). As regards the letter Ta’a, if it is added to the word “Allah,” it only means swearing by Allah.
[The Fatwa Center at Islamweb]