The sense inventory in ODE is essentially a reshuffled version of NODE/DIMAP. The number of senses is the same. I have followed ODE's numbering and division. The ODE sense inventory is mainly adequate; I’ve introduced only one new sense, though I have lumped a few FrameNet senses in with existing senses as an alternative to spinning off more new senses.
Quirk (esp. in ¶9.30) gives his summary of "over" senses, breaking them out somewhat differently than ODE does. He takes a more functional than a syntactic approach. In particular, he notes the "over" of accompanying circumstances, which ODE lumps with the "over" of duration: thus ODE classifies "over coffee" with "over the last five years" under the same sense, which is perhaps not entirely helpful. Another contrast: Quirk notes as "destination" (¶9.23) the sense that ODE identifies, uniquely, as purposeful: "so as to cover or protect." Thus the sentence "He threw a blanket over her." is destination for Quirk, and "so as to cover" for ODE. In this case, I think ODE’s take is probably more helpful because it associates this sense of over with purposeful actions — a feature that is generally not found in other senses.
ODE's core senses of over are probably a good summary of what this preposition does: Senses under core sense 1 are mainly about relative location; senses under 2 treat relationships among entities in which "over" is a metaphor for dominance (though the core sense is literal and concerns spatial relations); 3 (which has no subsenses) is about quantity or degree; under 4, movement is the theme, with much affinity with "across and through." The remaining core senses have no subsenses.
Notes from the spreadsheet:
New sense added: (Spreadsheet record 17) Though it corresponds to only two FrameNet sentences, this sense seemed worth breaking out separately because it exemplifies a use of over that has probably developed because it combines several of over's nuances, each of which, taken alone, would probably be covered by a different preposition. The specific meaning here is "by means of the resistant surface constituted by," or to supply an example: He was breaking bottles over my head. Thus one's head is the means of breaking bottles (the "means" aspect), the resistant surface that makes it possible (the "obstacle" aspect), and also the thing that is vertically lower than the POA (the "spatial" aspect). No other ODE sense of over conveniently subsumes this.
Other instances of over that may deserve idiomatic treatment
The phrases noted in ODE are not all prepositional but probably deserve looking at to avoid parsing over as a preposition where it doesn’t really act like one: as in the phrase be over. Concerning the phrases that are prepositional: over against (two senses) is probably better inherited by "against" for the first sense, and by some oppositional construction, not necessarily prepositional, for the second sense. over and above can be inherited by some of the core senses of "beyond."
Over supplies the second term in a number of phrasal verbs requiring a complement that might be construed as PPs, but are probably better not treated as such since the contribution of over in such cases doesn't correspond closely with one of its prepositional meanings: carry over, give over, hand over, knock over, pass over, pick over, roll over, walk over. Some phrasals in which over, though not really prepositional, might be construed as contributing one of its established meanings: boil over 12(4a); chew over and talk over, 16(7); go over 11(4); paper over and watch over 2(1a); take over 6(2b). Some phrasal verbs of motion using over mainly correspond to one of the "movement" senses in ODE: come over, cross over, run over.
I have assigned two senses the same SRType: 1(1) and 4(2) are both designated “ThingSurmounted.” I’m not completely clear on why ODE separates them, but in any case, I don’t think we lose anything by treating them as equivalents. Both involve relative orientation in space (i.e., one thing being above another) and don’t seem to take in any other idea that is semantically pertinent. Sense 2 notes the idea of “levels” (which is the basis of all the subsenses involving dominance relationships), but in a way, the idea of levels is implicit when one thing is above another, so perhaps is already present in sense 1.