All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
On one hand, if you (Questioner) sworn by W’ahduAllah (by the covenant of Allah) or by WmethaquAllah (By the covenant of God) and the like and bound your intention with them as oaths, then they have the same conditions and rulings of an oath such as: oath’s expiation and the obligation to fulfill it. However, if you didn’t bound your intention with the aforementioned statements as oaths, they will be considered as promises and you won't be obliged to offer oath’s expiation, since Al-Imam An-Nawawi (May Allah have mercy on his soul) said (What means):”Saying W’ahdullah , WmethaquAllah and W’amantouAllah doesn’t entail a person to considered them as oaths save if he bound his intention with them as ones.” [Rawdat At-Talibeen vol.11 pp.16]. For further details as regards oath’s expiation in details, kindly refer to Fatwa No. (346).
On the other hand, if you didn’t make an oath by W’ahduAllah and said instead: O’ahduAllah (I covenant Allah) or Ou’ahdka ya Rab (I covenant You God) and the like without using oath’s W, then the latter statements won’t be considered as oaths and you won't be obliged to offer oath’s expiation, yet you should be committed in fulfilling your covenants and avoid breaking them, since Allah, the Exalted said (What means):” Fulfill the covenant of Allah when ye have covenanted.” [An-Nahil/91]. And Allah knows best.