A Skylark wounded in the wing A Cherubim does cease to sing. (15-16)
When a bird gets wounded, an angel gets hurt too—that's what Blake is saying. Since "all that lives is holy" (in the words of Blake's "The Marriage of Heaven and Hell"), a bird is as important in God's eyes as a human or an angel.
The Caterpillar on the leaf Repeats to thee thy Mother's grief. (37-38)
This is a complicated one—apparently, the caterpillar reminds people of Eve, the "Mother" of humanity, whose sin in eating the forbidden fruit led humanity to fall from Eden. For Blake, the fall from Eden caused the creation of the natural world (which is really an illusion) and the descent of the spirit into lower life forms (like caterpillars, which feed off the natural world).
Man was made for Joy & Woe; And when this we rightly know Thro' the World we safely go. (56-58)
If you're not expecting everything to be sunshine and roses, you'll have a better time—you'll be prepared for suffering and won't have a lot of faulty expectations.
Every Tear from Every Eye Becomes a Babe in Eternity. This is caught by Females bright And return'd to its own delight. (67-70)
This is another complex mini-poem in itself, but basically it's saying that suffering is eventually redeemed. Sorrow will give birth to delight, at some point.
The Bleat, the Bark, Bellow & Roar Are Waves that Beat on Heaven's Shore. (71-72)
This might mean that the cries of suffering and anger experienced on earth lead to some sort of reaction in heaven—probably redemption.
The Strongest Poison ever known Came from Caesar's Laurel Crown. (97-98)
Blake is restating the old principle that absolute power corrupts absolutely, and the desire for power is particularly poisonous.