Hi, Arjun - 

So first, I recommend you read the paragraph under ConnectApi.FeedElementCapabilityInput in the Apex Developers Guide (http://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_connectapi_input_feed_element_capability.htm). 

Basically, you don't create a "poll"; you create a normal post (a ConnectApi.FeedItemInput or FeedElementInput object) and set its capabilities property to a new ConnectApi.FeedElementCapabilitiesInput object.  Now you can add any capabilites you want to that post, including polling, just by adding instances of the associated CapabilityInput classes (e.g. PollCapabilityInput) to the FeedElementCapabilitiesInput object you created. 

The project I was working on when I asked this question got cancelled, so I never did find out how to use it to respond to a poll.  But I have posted some code below that should allow you to at least create a poll.  I will warn you that it's never been tested (because cancelled) but I'm reasonably confident it will work, and I've added some comments to help you expand on it.  Hope it helps!!

Best,
Doug
 

public ConnectApi.FeedElement createPoll() 
    {
        // Create the poll and give it some choices.
        ConnectApi.PollCapabilityInput pollCapability = new ConnectApi.PollCapabilityInput();
        pollCapability.choices = new List<string> { 'Choice 1', 'Choice 2', 'Choice 3'};
        
        // Create a new ItemCapabilities object, and add the poll as a capability. 
        ConnectApi.FeedElementCapabilitiesInput itemCapabilities = new ConnectApi.FeedElementCapabilitiesInput();
        itemCapabilities.poll = pollCapability;
        
        // You could also add other capabilities (Files, Content, DirectMessage etc.)  
        // Some are displayed, while others (like DM) are behaviors.
        
        // Now create the parent feed item input (called 'input' because it's before posting; after posting it's a feed element).
        ConnectApi.FeedItemInput feedItem = new ConnectApi.FeedItemInput();	
        feedItem.feedElementType = ConnectApi.FeedElementType.FeedItem;		// This is the type for a normal post.
        feedItem.capabilities = itemCapabilities;							// Add the list of capabilities to the feed item.
        
        // That takes care of creating the Poll part of the post.  
        // Now let's finish it up with some message text, and direct it to a specific user.      
        
        // The message body is the main part of the message.  It consists of a series of segments (objects that inherit from MessageSegmentInput).
        // There are segments for Text, Images, Links, Hashtags, Mentions, etc.  Anything that can go in a post.
        ConnectApi.MessageBodyInput messageBodyInput = new ConnectApi.MessageBodyInput();        
        messageBodyInput.messageSegments = new List<ConnectApi.MessageSegmentInput>();
        feedItem.body = messageBodyInput;
        
        // Note that the parser will recognize hashtags or links in your text string, and convert them to link or hashtag segments for you.  
        // It will NOT recognize mentions ('@username'), so you must handle those yourself (see below).
        ConnectApi.TextSegmentInput textSegment = new ConnectApi.TextSegmentInput();
        textSegment.text = 'What choice do you want?';
        messageBodyInput.messageSegments.add(textSegment);

        // A mention segment is where you call out specific people who should see this.  (It's the equivalent of putting '@username' in a post.)
        ConnectApi.MentionSegmentInput mentionSegment = new ConnectApi.MentionSegmentInput();
        mentionSegment.id = '005RR000000Dme9';								// The ID (or username, but w/o the '@') of the user being mentioned.
        messageBodyInput.messageSegments.add(mentionSegment);				// Add a separate mention segment for each user mentioned (up to 25).
        
        // Finally, the subjectId is the ID of the user/group/record whose feed you're posting to (or 'me' to post to feed of current user.)
        feedItem.subjectId = '0F9RR0000004CPw';
        
        // Now that the item is all set up, we use the ChatterFeeds.postFeedElement() static method to post it to the feed.
        // The getNetworkId() method returns the user's community, or null if he is in the internal community or Communities aren't set up.
        // If you know you don't use communities, you can just put 'internal' or null.
        ConnectApi.FeedElement feedElement = ConnectApi.ChatterFeeds.postFeedElement(Network.getNetworkId(), feedItem);
        
        // Return the resulting element, in case you want to do something else with it, but you don't have to.
        return feedElement;
    }