Simply put, the oxygens' lone pairs are NOT delocalised into the benzene ring, and the stabilisation of the sulfonate group must be allocated more to ionic interactions(or loss of such; see below) than to resonance effects(the latter of which does not really matter that much, due to the instability of the "toluenide anion"-containing resonance canonical).
As many people have pointed out in many different answers posted on this site, there are no double bonds in sulfate groups and the like- the sulfur has a +2 charge while the oxygens have -1 charges each. These charges attract each other, resulting in the "double-bond-like" sulfur-oxygen distances. If an electrophile attacks and bonds to the oxygen, then the oxygen would not be able to have a negative charge anymore, resulting in destabilisation from the loss of an electrostatic attraction interaction.
Now, both nitric and toluenesulfonic acids are strong acids. In the nitrate case, there are two factors (pi-resonance and (+1 charge nitrogen)-(-2/3 charge oxygen) electrostatic attractions at work here, while in the sulfonate case, there is only one factor at work here, namely the (+2 charge sulfur)-(-1 charge oxygen) electrostatic attractions. Note that the elctrostatic attractions in the sulfonate anion are much stronger than those in the nitrate anion.
The destabilisation of the loss of electrostatic attractions upon protonation of the former is nearly of the same order of magnitude of the destabilisation from the disturbing of the pi-system upon protonation of the latter(if any, since the proton certainly would not want to attack the pi-system and violate VSEPR theory), and hence both acids become nearly equally strong acids.
Note: all of the above is true because the "toluenide anion" is unstable. In situations like the trifluoromethanesulfonate anion, the three oxygens' sp³ lone pairs, in the same direction as the carbon-sulfur bond, CAN delocalise into the sulfur-carbon antibonding orbital(which is mainly of sulfur 3p character; remember that one side of a 3p orbital has one node, just like the whole of a 2sp³ orbital), since the "trifluoromethanide anion" is relatively stable due to the inductively electron withdrawing fluorines. In support of this argument, optimisation calculations done on Mopac using the PM7 level of theory indicate that, while there is a charge <-1 on each oxygen in the toluenesulfonate anion(i.e. no delocalisation of the oxygen lone pairs), while there is a charge slightly >-1 on each oxygen in the trifluoromethanesulfonate anion(i.e. some delocalisation of the oxygen lone pairs).