You spend POW when the spell calls for it, as explained on the CRB (p. 243):
The spell cost is usually gauged in magic points and Sanity points; however, some cases (where an effect is long-lasting and/or highly significant) may also include a permanent expenditure of POW.
There are several examples of spells that allow you to cast them using POW instead of only magic points and/or sanity points, such as Blade Bless (5 POW; 1D4 Sanity points) or Contact Deity (5 POW; 1D6 Sanity points). While there are others that cost magic points, sanity, and POW, like Apportion Ka (10 magic points, 5 POW and 2D10 Sanity points per organ).
As for hit points, some spells allow you to spend hit points, either as an alternative to the spell's cost, or in addition to it. One example is the Gate spell, which says:
Using the Gate costs a number of magic points equal to one-fifth of the POW originally used to make the Gate. Each trip through a Gate costs 1 Sanity point. Should the user lack enough magic points for a trip, the traveller expends hit points to make up the cost.
And again, Call Deity, is another example:
Those who know the spell can sacrifice any number of magic points (including burning hit points).
The term burning hit points used here is not actually defined as an actual mechanic for spellcasting, and first shows up on the topic of Creating a new spell (p. 245), where it says:
Consider how easy the spell will be to cast. A caster might have 16 magic points and be able to burn some hit points to increase this number to, let’s say, 25. Beyond this, the caster will either require a reservoir of magic points or additional participants in the casting to donate magic points of their own. Some spells require POW to be spent. POW can be accrued by wizards through certain spells or items, such as an enchanted cane.
So, when a spell calls for burning hit points, the caster is allowed to sacrifice some of his hit points to fuel the spell as described under it's effects. But for spells that have no mechanics for burning hit points, it is simply not allowed as an option. Otherwise, it works as described under the CRB (p. 176):
Once an individual is out of Magic points, any further expenditure is deducted directly from hit points. (...) If Magic points reach zero, the investigator deducts further Magic point loss from hit points (one for one).