According to the Merriam-Webster online dictionary, a woe is "a condition of deep suffering from misfortune, affliction, or grief." In Sonnet 30, the poet Shakespeare expresses his woes in a number of ways, but it's important to keep in mind that he does it as a counterpoint to his conclusion at the end: that when he thinks about his beloved friend, his sorrows all go away.
When the poet mentions "the lack of many a thing I sought," he is sorrowful over things that he failed to achieve in his life. In the next line, he is sad about his "dear time's waste," emphasizing that the time that a person is given in life is precious, but he has wasted so much of it. He weeps for friends "in death's dateless night"—in other words, friends who have died and no longer live in the limited time of this world. He also cries over "cancell'd woe," or sorrows that have already passed and are already healed. He laments over "the expense of many a vanish'd sight," referring to people or things that he could see in the past but can no longer see.
The poet then repeats that he is remembering past sorrows: "grievances foregone," "woe to woe tell o'er," and "fore-bemoaned moan." These are all different ways of saying that he is not contemplating present sorrows but rather sorrows of the past. In the end, the thought of his friend takes all these woes away.