Some prefer to use the nebulous term, "nature" when referring to the demons and their godship or lack thereof. And that is fine, as long as we clarify what we mean by the word--"nature."
While trinitarians often like to make a demarcation between person and nature, John L. McKenzie writes that the apostle John was not aware of any such distinction. Indeed, prior to the fourth century--OUSIA and hUPOSTASIS were employed as synonyms (they semantically overlapped). It was this linguistic phenomenon that caused great confusion in the Christological controversies surrounding Arius. So certain church fathers saw fit to differentiate between OUSIA and hUPOSTASIS, so as not to speak heretically of God. But in the first century world of thought, the distinction between God's nature and person did not exist. McKenzie humorously says that the apostles did not know the word consubstantiality and could not even spell it. To speak of God and His Son in terms of a consubstantial relationship is therefore anachronistic and completely erroneous.
But there are other words that can be used to describe the nature of a thing. Aristotle used MORFH, FUSIS, and OUSIA to delineate the nature of a thing (RES). When constructing his hylomorphic theory of matter and form, Aristotle employed MORFH to describe the form of a RES (e.g., the matter of a table is wood, but its form is tableness). In other words, he utilized MORFH as a synonym for OUSIA. But his use of MORFH differed from the apostle Paul's first-century utilization of the term (where it means the "external shape" of a RES).
The Greek Scriptures express the concept of "nature" by employing FUSIS (instead of MORFH or OUSIA). The "divine nature" is QEIAS FUSEWS in 2 Pet. 1:4. What does Peter mean when he speaks of the "divine nature" that God's anointed would share in upon being resurrected to heaven?
FUSIS comes from FUW (to puff or blow, i.e. to swell up) and refers to growth, having an implied sense of genus or sort, native disposition or constitution (Complete Word Study: New Testament).
Thayer defines FUSIS as "nature," but goes on to point out a number of different usages for the term. They are as follows:
1. The nature of things, the force, laws or order of nature.
2. Birth, physical origin.
3. A mode of feeling and acting which by long nature has become habit.
4. The sum of innate properties and powers by which one person differs from another (See James 3:7 and 2 Pet. 1:4).
The entry FUSIS in BAGD also demands a careful study, so that one can ascertain what we mean by "nature."
In short, when I speak of the angels being gods by nature, I am using the word "nature" in the sense delineated by (4) in Thayer. Therefore, I am not speaking about the whatness of the angels when I say that they are divine by nature; I am talking about the "sum of innate properties and powers" that make them differ from humans. When describing the nature of beasts, Thayer refers to the "natural strength, ferocity and intractibility" that sets them apart from humans. This is not a delineation of their OUSIA (their whatness), but of their peculiar properties and innate powers that make them stand out from humans.
Addendum: I would now qualify the last statement above, but I'll let the post stand as written.