Well, you are not alone as most kids do this.
Even teens do this... so although older, they still have it in them. LOL
Anyway, try not to show that it is irritating you... try to stay neutral, show him proper ways or tones of voice to get what he wants or requests.
I always tell my son, who just made 3 years old: "Say it nicely, I know you know how...." and then, I make a poker face and wait. But I don't show irritation. I also taught him the word "respect." Then I wait... and then he giggles and says it nicely... just like he DOES know how. Then all is fine and I praise him. Then I reinforce "we are a team, right? Thanks for helping Mommy, & talking nice..." and then he tells me "My Mommy happy now...." and then he smiles and give me a big hug.
If my son does get whiney... well, I ignore it and reinforce "how do you ask politely???" and then I wait. And I wait. I wait and do other things... but I don't use any rewards/punishments such as food or time-outs etc., to get my point across. For my son, just knowing that I am either "happy" or "cross" is enough of an incentive for him. And then that way, he can become self-directed about it and yet still "express" himself.... but in a 'nicer' way. So he is learning about more positive communication.
MOST kids will whine at various ages. In different ways.
3 years old, can be hard... especially with communication and moods. So instead of concentrating on "rewards/bribes" or "punishments"... (for me), I concentrate on teaching positive/effective communication instead... and showing that it gets results. Good results. And I praise for it.
I allow for transgressions to a point.... meaning, as long as my kids are trying "their best...." then that to me, is a "result" I am looking for. I don't expect "perfection" EACH SINGLE TIME... but just tell them "try your best... how can you say it differently???"
And, when my kids are "faking" it... I tell them "I know you are faking it..." Period. Then they know they can't yank my chain or press my buttons. I also tell them "I can't read your mind... so tell me, nicely, so that I understand..." what you want.
Or, I tell them "how can you problem solve that? If you don't like something or don't want something... then how do you say that, INSTEAD of whining?" Then I wait. Then they think and I see their wheels turning... then my son, will typically change his tone-of-voice. And he gets proud. Then we 'high-five.'
That way, they can be a PART of the communicating, instead of being just talked "at" about it. Then they learn.
Kids will learn about "rudeness" and HOW to be polite over time, but not over night. At this age, they are still learning about socialization and are not experts yet.
A real great book is "Your 3 Year Old" which you can get from www.amazon.com It is a series of books for each age-set and describes the quirks/behavior of each age in an easy to read way. Although written years ago, it is STILL very pertinent.
Just keep reinforcing, in positive ways, about being polite and HOW to communicate. And yes, even if it means ignoring it until he stops, then do so. OR, ask him "WHY do you do that???" and in the case of my daughter, she's given me explanations I never would have thought of... sometimes she is just fed-up with me too... because maybe previously in the day, I was too busy to recognize a need in her. And then, she acted out about it, later. A 'delayed" reaction to it. So its interesting.... and I learned from her too.
I would not however, use "food" as a punishment or reward. Food is food... and it should not be brought into the realm of "emotion" based eating or not. Make meal-times "fun" and not about just eating a quota of food for eating sake. Or kids get hang-up about food and meal time. In time, they will try other things. My Mom, used to "make" us eat liver... she liked it. But not me. As a child, I hated dinner for that reason. Each person, child or not, has food preferences, and it changes throughout life. As I child, I would NOT EVER have eaten "liver" at-will... just because. I rather starve that eat that. Even now. So even if my Mom punished me for not eating liver... well then, so be it. Its not fair, though.
All the best,
just some thoughts and what I do, that have worked with my kids,