In a 74HC14 Schmitt trigger IC, unused inputs/outpus

The 74HC14 isn't TTL, it's CMOS, and what matters is that the input pins be kept from floating.

The reason is because the impedance of the input pins is so high when they're floating that random charges accumulating there can/will cause unpredictable internal behavior in the chip, including oscillation and high power dissipation.

The outputs don't need to be terminated since they're low impedance and they never really float, (being connected to either the high or low rail internally) their states being determined by whether the inputs are terminated to the positive or negative rail.

The output pins are being driven by the schmitt trigger; you should never tie a (non-tristated) output to a rail, and it won't do you any good here.

Because these are schmitt triggers, leaving the inputs floating is less harmful than would be the case for regular logic, but it's still a good idea (and free!) to tie them all to ground or VCC.