Which words in that passage are not easily understandable? The most "obscure" one that I can identify is "notwithstanding" (Google gives 48,000,000 results for "notwithstanding", so it is not exactly an obscure word).
A failure to understand that passage is a failure of comprehension, not of vocabulary.
Understanding the English-speaking world's most famous poet and playwriter might be beyond the abilities of some people, that is for sure. It doesn't mean, though, that the language used is deliberately obscure.
I would estimate that most high school graduates in the UK could correctly parse the passage posted, given enough time.
Those with education specifically in English would parse it at first pass.
Honestly - I don't understand anything. Imagine you had an English text with half the words substituted with Dutch ones (that look similar but make no sense).
So you might think you understand 2-3 words in a row only to come across the fourth word that seems key for the line but means nothing to you in the given context.
What makes it harder to understand is not the vocabulary, but the grammar, as well as Shakespeare's sometimes idiosyncratic use of word meaning. For example, "strain" here means a portion of music, which while not its most common meaning, is certainly within the abilities of most educated native speakers of English to understand, at least from context.
That's exactly what I mean - words that we otherwise know are used with completely different meaning, which renders the text unintelligible.
I disagree with you completely that 'most educated native speakers' can understand this. By the same token one can say that most native English speakers can solve differential equations :)
The definition of strain you mention is #30 in the dictionary - http://dictionary.reference.com/browse/strain. Can you cite its use in that meaning in a contemporary newspaper or magazine?
As to usage of "strain" in music, a quick search lead me to this article from the US dated 16 Feb 2015 [1] "When the trumpets blare and the snares rattle during the opening strain of John Phillip Souza’s The Washington Post March..."
I not proposing that Shakespeare is the easiest thing to read, but merely suggesting that it is not as inaccessible as it might first appear.
If music be the food of love, play on;
Give me excess of it, that, surfeiting,
The appetite may sicken, and so die.
That strain again! it had a dying fall:
O, it came o'er my ear like the sweet sound,
That breathes upon a bank of violets,
Stealing and giving odour! Enough; no more:
'Tis not so sweet now as it was before.
O spirit of love! how quick and fresh art thou,
That, notwithstanding thy capacity
Receiveth as the sea, nought enters there,
Of what validity and pitch soe'er,
But falls into abatement and low price,
Even in a minute: so full of shapes is fancy
That it alone is high fantastical.