Learn English – the meaning and origin of the common phrase “the world is your oyster”

Etymonline reports that straight to mean "true, direct, honest" is from 1520s.

One of the colloquial definitions of grind is (from the Oxford English Dictionary):

Steady hard work; labour of a monotonous kind, esp. close and hard study; an instance of this, a dull and laborious task.

The first written use of this is:

1851 B. H. Hall Coll. College Words, Grind, an exaction; an oppressive action. Students speak of a very long lesson which they are required to learn, or of anything which is very unpleasant or difficult to perform as a grind.

So the grind of one's day would be the daily, monotonous work that one has to do. It is more common to refer to this as the daily grind.