The shapechanger ability description for changelings in Eberron says that you must adopt a form with the same basic arrangements of limbs. Would this definition extend to wings and tails and the like as well?
It really depends.
The "basic arrangement of limbs" is talking about being, for example, a bipedal four-limbed bilaterally-symmetric creature. That is to say, you have two arms and two legs, and your right and left halves are more or less laid out the same but mirrored.
A changeling can't turn into, say, a wolf, which has the right number of limbs but in a different arrangement (i.e. four legs, no arms). They also couldn't become a four-armed thri'kreen, because the changeling doesn't have six limbs to start with. I would think this also excludes any sort of "angelic/draconic wings" situation, since wings that are distinct from the arms would represent a whole extra set of limbs, and that doesn't fit into the "same basic arrangement" restriction.
However, if your changeling were, say, a 14th level draconic sorcerer, with the ability to "sprout a pair of dragon wings", then they could indeed imitate any other back-winged creature (but still not a thri'kreen).
However, if the target creature has wings for arms, like a harpy or some sort of bird-folk, that shouldn't be a problem to duplicate. They won't be functional wings, of course, but there should be no issue with turning your arms feathery for the purpose of a disguise.*
As far as tails, it'll probably be up to the DM, but I see no reason to restrict them. It should be fine to give yourself a tail as necessary to impersonate lizardfolk or something. If you want to get really technical, a tail isn't a limb as such, but an extension of the spine -- or to be more accurate, the human spine ends in a tiny vestigial tailbone -- so a changeling would have all the anatomical parts for a tail even though it's completely internal in many humanoids.
*Aarakocra are weird on this front. The art and descriptions up to 3rd edition gave them wing-arms, but as of 5e, the art depicts aarakocra as having both arms and wings as separate limbs, presumably to simplify running them as monsters without wondering whether or how they can draw and throw weapons while flying.
It depends on the wings you want and what the form you are starting from is
The relevant rules text that we need to interpret is:
[...] You can make yourself appear as a member of another race, though none of your game statistics change. [...] you must adopt a form that has the same basic arrangement of limbs that you have. [...]
The key word in the last sentence is "limbs".
Since 5e uses natural language for it's rules text, the understood meaning of limbs in English is summarised best by this Wikipedia entry:
A limb (from the Old English lim), or extremity, is a jointed bodily appendage that humans and many other animals use for locomotion [...], or for prehensile grasping or climbing.
So, in the case of a changeling, their basic arrangement of limbs is that they have 4 limbs (2 arms and 2 legs) with 2 used for locomotion, and 2 which can be used either for grasping/climbing or for locomotion (you can propel yourself using your arms and legs should you so choose). If they are granted more limbs via magic or some other game feature, but retain the racial abilities then obviously that would increase the number of limbs their final form can have.
You can't increase or decrease the number of limbs you have, and their basic arrangement needs to be in roughly the same location on your body (2 near the head and 2 near the rear).
So, you can't, become a winged demon or angel, as the wings of those forms are additional limbs. You could, however make yourself look like an aarakocra that has lost it's arms, or one whose wings and arms are the same limb.
Notably, the restriction on your game statistics not changing comes into play here too. In particular this means you cannot gain or lose methods of locomotion, so you don't gain a flying speed by making yourself look like a race with wings (but if you already have a flying speed due to magic or some other game feature, you would retain that flying speed in your new form for the duration that you would otherwise have had the flying speed).
As a happy note, you can, change your appearance to add horns or a tail or other cosmetic appendage. So long as you don't try to use the cosmetic appendage as a limb it's fine. So for example, you can't give yourself a prehensile tail that can grab and manipulate things, but you can give yourself a tail. So for example, you can give yourself a cat or dogs tail, but you cannot give yourself a fully functioning monkey tail (but you could give yourself a suitably non-functioning tail that looks like a monkey tail).
If you cannot fly, you can give yourself non-functioning wings, so long as they aren't additional limbs (ie they are incorporated into the number of limbs you currently have, so combined "arm-wings" would be fine). If you can fly, then you can give youself functioning wings for the duration of the time you can fly (still subject to not gaining additional limbs).
Horns, tails, and other cosmetic appendages are perfectly fine, so long as you stick to them not being able to do anything a limb would do (so no grasping with your tail, and no trying to use your horns as natural weapons).
A note on Aarakocra wings
While the 5e art shows an example Aarakocra with angelic style wings, it is just that an example, it doesn't preclude other wing shapes within the race. In fact, the description for the race notes a huge amount of variation is possible:
From below Aarakocra look like large birds [...]. Standing upright [...] they have long, narrow legs that taper to sharp talons.
Feathers cover their bodies. [...]. Their heads complete the avian appearance being something like a parrot or an eagle with distinct tribal variations.
So the description does not preclude different arrangements and combinations of wings/arms.