In Hindi there is no frozen rule as to the order, because you can easily understand what's the subject, what's the object and what's the verb. The rule is SOV but that can change if you want to emphasise something. Here कौन is the subject, if it was चाय the verb would have been पीती (चाय is feminine) and the sentence wouldn't have had sence.
There is no oblique case here because there is no postposition.
'Whom is the tea drinking' (as in, the bizarro universe sentence where the tea is doing the drinking and a person is being drunk) would be 'चाय किसको पी रही है'.
किसको (or its alternate form किसे) is the dative form of कौन. You will probably find it easier to understand the sentence when you consider the possible responses to the question - चाय नेहा को पी रही है (The tea is drinking Neha), चाय उसको पी रही है (The tea is drinking him).
Note: किसको/किसे is also the dative form of क्या (what). So, the sentence चाय किसको पी रही है can also mean 'What is the tea drinking?'.