The anonymous "The Wanderer" contains irony in regards to the fact that although the Wanderer feels as if he is alone, he is not. Throughout the first part of the poem, the Wanderer laments the fact that "there are none now living" which he would share his feelings with. The Wanderer, far from home, finds no one with whom he can share his innermost thoughts with. No one whom he loved is left. All are gone.
The Wanderer traverses the seas, hoping to find someone who knew his people. No friend could be found. The Wanderer states that "all the joy has died." Yet, one thing the Wanderer (and all of mankind) comes to understand is the power of God. While everything around him is fleeting (money, friend, man, and kinsman), God remains.
The irony, then, lies in the fact that the Wanderer wanders the sea looking for one with whom he can share his emotions and secrets with. The entire time, God was (essentially) right there. The wise man, according to the poem, always keeps his faith. Therefore, the irony lies in the fact that the Wanderer was searching for something (God) which was with him the entire time.