"springes to catch woodcocks..."
See in text (Act I - Scene III)
A "springe" is a snare to catch small-game, such as the woodcock, a small wading bird. Polonius characterizes Hamlet as false and, through the use of the hunting metaphor, predatory. He compares Ophelia to a game-bird and suggests that Hamlet is attempting to lure her in with his vows and tenders, only to snare her. Both Laertes and Polonius characterize Ophelia as unsuspecting and passive, emphasizing the lack of agency, especially sexual agency, that women had.
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"to be demanded of a sponge..."
See in text (Act IV - Scene II)
Hamlet explains this metaphor more fully in his next passage, where he states that as servants to the king Rosencrantz and Guildenstern suck up his attention (and suck up to him). In the line, sponge seems like a sneering insult, and one can imagine Hamlet delivering it with disdain.
"That I might be the organ...."
See in text (Act IV - Scene VII)
Here "organ" means "instrument," in the sense that Laertes wants to be the instrument in Claudius' plan to kill Hamlet. Though he's asking for the opportunity to be used, it should be noted that Claudius has manipulated him into doing so. In reality, Laertes has already been "played" like an instrument in a way that Hamlet can't be.