It's worth thinking a bit about how the IPA table is divided and the motions underlying these sounds (i.e. gestural phonology).
We have places of articulation, and manners of articulation.
If your elves' have vocal tracts with analogous structures (moving backwards: lips, teeth, alveolar ridges, hard palates, soft palates, uvulas, pharynxes, and glottises) then the same places of articulation will exist. If you have additional structures, you'll have additional places of articulation, and if you're missing some structures you'll have fewer.
Now methods of articulation. There are four main articulators involved in speech, each of which allows for the production of sounds in a different set of places of articulation. These are the lips, the tongue, the pharynx, & the glottis.
Each articulator can produce a variety of gestures:
- Complete closure: this gives stops, taps, and trills
- Close restriction: this gives fricatives
- Open restriction: this gives approximants and vowels
The tongue, and to a lesser extent the lips are very flexible and can contact multiple places of articulation. In humans, the lips can contact the other lip, or the teeth, whilst the tongue can contact anything from the lips to the uvula. If your elves have especially short lips, or lack the overbite common in humans today, they might find labiodontals difficult and lack them, and if they have short tongues, they are unlikely to have linguolabials, or even dentals.
Additionally, these articulators are able to form a variety of shapes and can use different parts of themselves to make the articulation. This gives the difference between retroflex and alveolar consonants (are you contacting with the top of the tongue, the tip, or even the bit just below the tip), between sibilants & non-sibilants (is the tongue flat or grooved), and between laterals and non-laterals (is the restriction made with the edges of the tongue or the centre). In natural languages, these shape contrasts are only observed with the tongue as articulator, but if your elves have especially bendy lips, they might be able to produce analogous contrasts with their lips.
The glottis and pharynx are fairly restricted due to their very nature, both only being able to act in their respective place of articulation, but you do have some freedom here in terms of what articulations they can actually produce. Human glottises can produce stops or fricatives, but the pharynx cannot produce stops. Perhaps your elves are able to fully close their pharynx (not only would this allow for pharyngeal stops, it would also allow for a new secondary articulation, intermediate between clicks, which use a velar closure, and ejectives, which use a glottal closure).
In humans, because our jaws are hinged at the back, fully open restriction is only really possible from the soft palate forwards. This is why the distinction between approximants and fricatives starts getting fuzzy around the uvula and back, the open restriction & close restriction are just too nearby for the clumsy back of the tongue, or the pharynx, or glottis to reliably distinguish them (likewise, vowels are articulated exclusively in the space between the alveolar ridge and soft palate). If your elves have mouths that swing open in such a way that the back is as open as the front, they might be able to reliably distinguish uvula fricatives from approximants.
In addition to these main articulators, there are a couple of other things to consider. These are the vocal chords and the nasal cavity.
Vocal chords give you the ability to distinguish voicing. Humans have tremendous control over our vocal chords allowing for languages that distinguish many different phonations (modal voicing, voiceless, creaky, breathy, etc), as well precise differences in voice onset time (voiced, tenuis, aspirated). If your elves have even finer control they may be able to distinguish even more levels, and if they have weaker control, they may distinguish fewer, or none at all.
The nasal cavity allows for nasal sounds. Gesturally, nasals aren't a separate method of articulation, but a secondary articulation on top of a voiced stop (the same secondary articulation that would go on a nasalised vowel, approximant, or fricative). In nasalised sounds, the very back of the soft palate (around the uvular) lowers, allowing air to enter it at the same time as it enters the mouth, this adds an additional resonating chamber giving an extra overtone visible in a waveform. Because the back of the soft palate has to lower to produce them, nasals are most easily produced forward in the mouth, are difficult on the soft palate, and impossible further back than the uvula. If your elves' nasal cavity connects further forwards than humans, they might find velar or even palatal nasals difficult, if it connects further back, they might find uvular nasals easy, and have an additional series of pharyngeal nasals even further back that they can produce but find difficult.
Any other changes to the vocal tract will affect the timbre of the sounds produced, but not what the sounds actually are at a gestural level (or how they would likely be perceived by a human with some exposure to the language). Many of the changes discussed above (especially adding or removing structures from the vocal tract) will also affect the timbre. As it is, it sounds like all the differences between your elf vocal tract and a human one are of this type.