Some humans in our world have multi-coloured eyes, known as heterochromia. There are various different types, full, sectional and central. This happens due to various amounts of melanin being produced in the eyes. People may be born with heterochromia at birth or it may develop some time afterwards. It is possible to have multiple types of heterochromia.
Full or complete heterochromia is where a person has two different coloured eyes, such as one blue and one green. This is the most visibly obvious of the three and the one people commonly associate heterochromia.
Sectional or partial heterochromia is where a small segment of the eye is a different colour than the rest of it. Often it only affects one eye.
Finally central heterochromia is where there is a ring of colour around the iris which is different than the rest of the eye. To use myself as an example, my eyes are primarily green but there is a ring of brown that looks like it bursts out from the centre. Often it affects both eyes but it is possible that it could only affect one.
As someone with a form of heterochromia, I can safely say that having two different colours in my eyes does not affect my vision in the slightest. However, I have noticed my eyes are more photosensitive than those of my peers. I don’t know whether that's because of the heterochromia, simply because they are in dark colour or because I spend most of my time indoors in a dimly lit room behind a screen, though I would assume it is the latter.
Applying to your Question
Your question is essentially asking for an active version of heterochromia, in our world it doesn't change, your eyes remain the same colours, you don’t wake up one day with brown eyes and the next with green (however, as the pupils dilate and contract, more or less of the colour is exposed. In my case, it's hard to see the brown if my pupils are fully dilated and easier if they are fully contracted).
It is possible that your humanoids can actively (if subconsciously) add or remove melanin from the eyes. This would cause them to change colours. Certain emotions may dictate where the melanin goes, such as full heterochromia to show confusion or changing the eyes to a dark colour to show anger or fear. Using heterochromia as your basis, you could get some pretty complex emotions based on the colours and/or patterns.
Below are some examples of heterochromia:
(Note that although most people in these images are white, heterochromia can be found in every ethnic group. Heterochromia can also be found in some domesticated animals, such as cats and dogs.)