Written in 1603 at the death of his seven-year old son, Ben Jonson's style in "On My First Son" is particularly powerful for what it meant within that society to lose a male child at that age. The seventh year was the time when a girl and boy would stop wearing similar clothes (smocks, for instance) and boys would be "breeched" or wear pants ("breeches"). It was also that point when the boy's education would become more formal, leaving behind the school room or nursery where a woman would have instructed him, and entering into the world of education at the hands of a man—a tutor, teacher in private school, etc. In a sense, this is a "rite of passage." It is at this important time, with so much ahead to join father and son, Jonson's son dies.
In terms of the tone Jonson adopts, here it is much different than the manner in which he was accustomed to writing, "usually more cynical or mocking."
Looking to literary devices in the poem, here are a few I have noticed. First, an allusion is used. Allusion is when there is a reference to a famous person, place, event, etc. In this example, the allusion is to the son of God: Jesus.
...child of my right hand...
The Apostle's Creed refers to Christ who "sitteth on the right hand of God the Father Almighty..."
...“and joy” offers an ironic subtextual biblical allusion to Rachel’s name for her son Benjamin, which was Ben-oni, or “child of sorrow.”
There is a metaphor which compares Jonson's parenthood to a loan. (Remember that a metaphor is when two things are compared as if they are the same thing, but which only share similar characteristics.)
Seven yeeres tho' wert lent to me, and I thee pay,
Exacted by thy fate, on the just day.
Jonson's son had been lent to him for a term of seven years, like the length of a loan, and when the agreement was reached, Jonson was forced to return the boy to heaven, from where he had been granted the "loan" of the child in the first place.
There is also a paradox. A paradox is a statement that contains a kind of truth, but which at first seems self-contradictory and untrue. Jonson writes:
Will man lament the state he should envie?
There is a contradiction between lamenting and envying: we might at first ask how it is possible that we should envy something which causes us grief or sorrow. In the poem's context, we understand that losing the boy causes grief, when knowing he is in heaven should make a Christian envious.
Rest in soft peace...
...is a form of imagery, giving "peace" the attribute of being "soft" (as opposed to "hard").
Last, I would suggest there is an irony in the last pair of lines with regard to Jonson's "future note-to-self" as to how he should protect his heart:
For whose sake, hence-forth, all his vowes be such,
As what he loves may never like too much.
It may be that Jonson is reminded of the temporal nature of life... that in loving things—when we "like them too much"—it is all that much more painful for us when they are taken from us, as Jonson's son was.