Sadly, I don't think that whining is a stage. DD is 26 months and still driving me crazy with it.
What you're describing sounds like it could definitely be a milestone-type thing though. Lots of kids get really irritable when they're about to reach a big milestone. Every time DD is about to shoot up an inch she just stops eating and becomes a horror at the dinner table. Of course, this doesn't mean that you have to just deal with it.
Your DS may still be young for this, but we're working on the whining for my DD. When she starts whining we tell her that we can't understand her when she speaks in a whiny voice and if she needs something she needs to ask in a normal voice. She seems to be getting it a bit, but it's still a constant battle. Something else that worked well when she was younger is getting her in a situation where she can just do whatever she wants. Our local children's museum works well for that, or you could just make a room that's filled with only things that DS is able to play with and have fun with (even things that aren't normal toys like letting him open drawers and what not) and just let him go to town. Just the running around having fun without having any correction seems to put them in a better mood.
Also, something that helps for me is to just step back. My rule of thumb is that if it's not going to send her to the hospital, it's okay. Some parents may not agree with this, but I feel like life is happier for the both of us if I try to let her be free as much as possible. Sure, it's probably not "proper" to let my toddler jump on the table. Sure, she may fall off and cry, but guess what? I'm here to comfort her and she'll be fine. Much easier and happier to not fight it.
Also, I try to think of tantrums as a normal part of toddler life. It's annoying and I hate it when she freaks out in public, but that's how she's expressing an emotion. She doesn't understand that her anger/frustration should only be released in certain ways. She understand that she's angry and not getting what she wants and she feels like flopping on the floor and screaming. Honestly, I can empathize. Sometimes when I don't get what I want I feel like hitting the wall or screaming at the top of my lungs. The only thing that stops me is that I am an adult and I understand how to control my actions. I don't expect this from a toddler. She's just barely understanding what these feelings are, she can't be expected to control them. So what I do is let her have her fit (generally for her it's the flopping on the floor screaming) and I tell her to let me know when she's done. I know many parents of children that are similarly aged to DD (or have seen it in the past) who will sit there and fight with their child who is already having a fit and it ends up being 20 minutes of screaming and everyone is worse off. For DD, she'll scream and get upset for a minute or two, but then she's done. She has it out of her system and honestly, I wouldn't even know that she's just had a fit a minute later. She's happy and running around again like nothing happened and I think it's because she got the feeling out of her system and feels better. Of course, if she's hurting someone in the process of having the tantrum it's different, but it's generally me just telling her that's not okay and then removing her from the situation.
Sorry that was a novel. Hopefully it helps some!