"Strained" is a Shakesperean-era term for "forced or constrained"; it means mercy must be freely given. You can grasp this by seeing the quote in context:
The quality of mercy is not strain'd,
It droppeth as the gentle rain from heaven
Upon the place beneath. It is twice blest:
It blesseth him that gives and him that takes.
Portia is importuning Shylock to show mercy, but recognizing that she cannot demand it. Shylock declines, of course, and this proves his undoing, for now Portia uses his "letter of the law" attitude against him.
A modern-day equivalent would be something like
Look, I can't force you to give me a break here, but it would benefit us both if you did.
To "have mercy" is the plea of someone who desires mercy before it has been extended. The publican, or tax collector, who stood at a distance from the Jewish temple in Jesus' day, not so much as looking up to heaven "beat his breast and said, 'God, have mercy on me, a sinner'" (Luke 18:13 NIV). In this context, Jesus contrasted the words of a self-righteous Pharisee ("'God, I thank you that I am not like . . . this tax collector. I fast twice a week; I pay tithes of all that I get'") with those of the tax collector. He said, "'. . . this [tax collector] went to his house justified rather than the [Pharisee}, for everyone who exalts himself will be humbled, but he who humbles himself will be exalted" (ib., v.14).
In order to receive mercy, one must humble himself, thus acknowledging tacitly there is a reason why mercy should not be extended. If the person from whom one is requesting mercy is merciful, then mercy will likely be extended. There is a pithy statement that goes: "Grace is getting what you don't deserve; mercy is not getting what you do deserve."
In confining my search for mercy strictly to the Bible, I found the following expressions. In no particular order: "show mercy," "without mercy," "receive mercy," "great mercy," "full of mercy," "rich in mercy," "had mercy," "desire mercy," "love mercy," "withhold mercy," "with mercy," "request mercy," "cry for mercy," "lift up my voice for mercy," "gets no mercy," and "beg for mercy."
When someone asks another person to "have mercy," the implication is that a punishment, though deserved, can also be withheld, if the one who can extend mercy chooses to.
I remember seeing a movie--a "western"--years ago, in which a bad guy begs the protagonist (Clint Eastwood?) for mercy. The protagonist says wryly, "How is it that those who ask for mercy never give it?"
That reminds me of the ancient story of a debtor and his creditor. The creditor to whom the debtor owed a huge sum showed him mercy and forgave the debt. What did the ecstatic man who had been shown mercy do? He turned around and withheld mercy from one of his own debtors, who owed him a piddling sum. He then had him put in debtors' prison until the last penny was repaid. Ironic, isn't it?
Best Answer
It's describing God (I assume, judging from the capitalised Me), and using the analogy of an onion's layers.
If you take away the outer layer showing mercy, expecting to find cruelty underneath as the true nature, you don't: you find mercy. And if you scratch at that layer to get underneath, you find mercy again. He is mercy all the way through.
In this case, beauty is more than skin deep: it is the entire being.