This observation also stood out to Judith Jesch, who included it in a list of stimulating insights at the end of her informal review of Ash and Elm. Price says, in full:

One other dimension of the gods' lives is intriguing. Strangely, Asgard also contained temples, cult buildings where the gods themselves made offerings—but to what or whom? The mythology of the Vikings is one of only a tiny handful in all world cultures in which the divinities also practices religion. It suggests something behind and beyond them, older and opaque, and not necessarily 'Indo-European' at all. There is no indication that the people of the Viking Age knew what it was any more than we do. (p. 50)

The suggestions here exceed the evidence. Price might be on the right track in saying that the gods themselves made offerings (or more accurately, that one god made an offering to himself), but I can't confirm the surrounding claims.

In Price's bibliographic essay at the back of the book (alas! a poor substitute for footnotes and discussion, but increasingly the choice of publishers who think academic writing and public audiences can't mix), he points to his source: Kimberly C. Patton, Religion of the Gods: Ritual, Paradox, and Reflexivity, ch. 7: "Myself to Myself": The Norse Odin and Divine Autosacrifice (2009). Patton centers her chapter on the Icelandic poem Hávamál, which was first written down in Iceland in the 1200s, although some scholars and many enthusiasts have argued that it dates to Scandinavia in the 800s. (This would require the poem to be passed down orally and accurately for 400 years!) In the relevant strophes, Odin speaks:

(138) I know that I hung / on the wind-swept tree / for nine full nights, / wounded with a spear / and offered to Óðinn, / myself to myself; / on that tree / of which no one knows / from what root it rises.

(139) They did not comfort me with bread, / and not with the drinking horn; / I peered downward, / I grasped the runes, / Screeching I grasped them; / I fell back from there. (From Gabriel Turville-Petre's 1964 translation.)

This is a weird passage. At surface, it says that Odin sacrificed himself to himself to gain knowledge. Contrary to Price's claim that we don't know what the gods practiced sacrifice for, Odin is not making himself into a votive gift to an unnamed higher god—he names himself—and it's the process not the object of sacrifice that matters here. This is also the interpretation that Patton takes—Odin is participating in his own cult, and in other chapters she points to parallel examples from other cultures, such as Poseidon swearing by himself in The Birds and Jupiter joking that he'll offer libations to himself in Amphitryon. And, of course, Christ, as one of the three Persons of God, is similarly sacrificed by God to God. As Patton says, "The theology of the crucifixion reveals a powerful sacrificial circularity" (p. 309).

Now, Patton points to the diversity of her examples to suggest that there were Indo-European ideas about self-sacrifice that could have informed the Hávamál depiction of Odin's self-sacrifice, rather than direct Christian influence. I'm not convinced. The parallels are, as Patton admits, "intense" (p. 216)—both Odin and Christ hang from "trees", both figures are pierced by spears, both cry out prominently, both thirst, both descend from their trees—one to the knowledge of runes, the other to the Harrowing of Hell. Now, people in Viking Age Scandinavia certainly knew of contemporary Christianity, but their knowledge of classical Mediterranean mythology was sketchy at best. I have a hard time not seeing Christian influence here.

Patton supports her claim by asserting that the Hávamál stropes date from the 800s, presumably before significant Christian influence arrived in Scandinavia. (Nevermind the fact that there had already been Scandinavian-Christian contact for centuries.) Unfortunately, there's no corroborating evidence that people in Scandinavia talked about Odin's self-sacrifice during the Viking Age. Patton points to a Gotland picture stone, Lärbro Stora Hammars I, as one example, which she dates to the 700s. But according to a recent volume, the stone more likely dates to the 800s or later. And despite the potential references to Odin on the stone (namely the triangle axe and the bird), there's no image here of a god hanging from a tree. Patton also points to a more convincing example from—of all places—a church in Hegge, Norway, with a one-eyed wooden face sticking its tongue out as if strangled. But this carving likely dates to the 1200s, or the same post-Viking Age period when the Hávamál was also written down.

While Odin himself shows up in the archaeological record long before Christian material culture takes root in Scandinavia, our images of Odin's self sacrifice—the Hávamál and the Hegge stave carving—both date from after the Viking Age. The story as we have it in these sources was almost certainly influenced by Christianity. This story might have been invented or at least manipulated to help listeners understand Christian theology in different terms. Certainly the priests and parishioners of 13th-century Hegge saw no conflict in using a one-eyed strangled figure to help them reflect on the mysteries of Christ.

We can securely date this cultural cross-contamination to the 1200s, although I'd be willing to accept that it might date from as early as the late 800s, when northern pagans began to adopt other elements from Christianity to help them develop and articulate their alternative religious beliefs. The late 800s were, for example, when Thor's hammers became popular across the north, and these were almost certainly worn and used just like crosses, in part to articulate religious affiliation. One of my favorite examples comes from the burial of a war leader who died while the Great Heathen Army occupied Repton church over the winter of 873/4. This kind of behavior adopted Christian norms (churchyard burial with a t-shaped pendant) albeit in a violent rejection of Christian power.

So, going back to the question, the claim that Viking gods had their own gods is overstated, although it's definitely a reasonable inference from Price's phrasing. More concretely, did Viking-Age people believe that Odin and his kind practiced religion? Well, maybe, but only insofar as a god might participate in his/her own cult. If they held this belief, then it might have actually made the weird Christian story of Christ's self-sacrifice more intelligible and actually helped speed conversion along.