If I really want food right now, should I use the present continuous (I am wanting food) or the simple present (I want food)?
Since want is a stative verb (BBC Learning English website), in American and British English one would use the present simple tense.
Stative verbs describe states or conditions which continue over a period of time, so like, love, hate, want, need, hear and see would all be examples of stative verbs. These verbs are not normally used in the progressive form.
The present continuous would sound strange. I highly recommend the above link to BBC Learning English page on the topic.
To emphasize your state, you can say such things as
I really want food right now (as you wrote), or, more typically:
I'm really hungry.
I'm so hungry I could eat a horse. (American English)
I'm dying of hunger.
I'm very hungry.
Speakers of Indian English may use the present continuous, as they seem to use it with stative verbs more often.
Like other verbs of internal sensation or perception (eg think, feel, see) "want" is normally used in the simple present:
I want food.
But all of them can be used in the continuous when there is a special emphasis on the immediacy:
I'll talk to you later, but right now I'm wanting food.
I'm watching him on video; I'm seeing him open the door; I'm hearing the sounds inside ...
I don't think you ever have to use this form: it is optional, to express this immediacy, this "right now"-ness.
I am wanting food right now.
I want food right now.
As commonly used, the stative verb want should be in the present simple. It sounds strange to use it in the progressive, but it's not incorrect grammatically. According to Cambridge English Grammar Today, you can use the want in the progressive for indirectness or politeness. You can also do so to emphasize an ongoing or repeated process.
So you can say either I want food right now or I am wanting food right now. However, the former sentence in the present simple is preferable and more common.
The Free Dictionary also states the use of 'want' in informal English. It also states the use of want in the future progressive, the present progressive, and the past progressive in informal and formal English.