This is a difficult question to answer. A student of psychology will tell you that the two women, Sofya and Eveline, are suffering from psychological trauma and are not acting of their own volition but rather are being acted upon by the violence of circumstances or emotion or past memories: for Sofya, it is circumstances and Ilyin's violent emotion; for Eveline, it is past memory and the tyranny of terror.
Strictly speaking the best description of what Ilyin is experiencing is intense lust and intense desire to dominate. Frank might be said to be the one who will most honestly experience intense loneliness as he sails afar without the one he loves at his side as he dreamed of. His loneliness may perhaps be accentuated by intense regret and despair as the ocean rolls relentlessly past him.
Having said this, it is possible to interpret these stories as displaying awareness of intense human loneliness through each of the three principal characters. It might be said that Ilyin feels intense loneliness because of the unfulfilled yearning of his love for Sofya. This intense loneliness would be the result of his realization of there being a desperate end to his feelings if left unrequited (i.e., unreturned):
I shall put a bullet through my brains ... What am I to do if your image has grown into my soul, and day and night stands persistently before my eyes, ... what ... can I do to get free from this abominable, miserable condition ... ("A Misfortune")
It might be said of Eveline that her intense loneliness began when her mother died and she was thrust into positions that were not rightly her own. It might be said that her intense loneliness began with the loss of her mother and that it was deepened by the impossibly hard deathbed-promise her mother extracted from her.
As she mused the pitiful vision of her mother's life laid its spell on the very quick of her being--that life of commonplace sacrifices closing in final craziness. ... She stood up in a sudden impulse of terror. Escape! She must escape! Frank would save her. He would give her life, perhaps love, too ... ("Eveline")
Sofya's intense loneliness occurs only at the end of the story, only after Ilyin's intense and violent emotion has overpowered her. She feels the intense loneliness of being caught between two worlds in a psychological space that none other can enter and from which she can not escape to join, or rejoin, the world of genuine, sincere and unmanipulated sentiment and emotion.
she got up languidly and dragged herself to her bedroom. ... She sat down by the open window ... There was no "tangle" now in her head; ... She understood now how strong and relentless was the foe. Strength and fortitude were needed to combat him, ... and her life had given her nothing to fall back upon..... ("A Misfortune")
Maybe all three feel the same loneliness as Sofya feels. Maybe all three feel caught between psychological worlds where there is no one to understand, to share, to aid, to open a door into the world that others occupy with integrity of emotion and sincerity of expression.