Pit is a wonderful game, probably the best game released in 1904. I imagine that Wheedle came about by Knizia taking a look and saying to himself "that's interesting... but I think I can do better." And so he did.
Like Pit, Wheedle is a lightly-themed stock game, played in real time, where players are frantically trading cards with each other to try to collect sets of cards. Each card represents stock in one of several satirically-named companies (like "N Securities" and "Hard Cell Phones"), and players are trying to get at a majority share of as many companies as they can.
Unlike Pit, all trades are made with full disclosure. You say not only how many cards you are trading with other players, but also which cards. Trades can be uneven; you can trade one card for two, or you can even give away or accept cards in exchange for nothing.
Additionally, there is one face-up card in the center of the table (the deck has 61 cards, so there will always be one left over, whether you play with three, four, five, or six players). Anyone can trade one-for-one with the table at any time -- first come, first served. This does occasionally lead to disputes of whose cards are whose when several players put a card on the table to exchange at the same time; as players get more experienced at playing, this tends to happen less.
At any time, any player can end the round of trading. The game rules do not suggest a mechanism for this (and I have witnessed games where some players are concentrating so much on their hand that they do not notice that the round has ended), so you would be encouraged to supply your own bell, air horn, or some other sufficiently attention-grabbing device.
Scoring is as follows: for every company in which a player has a majority share, they earn one point per card; a player gets two points per card if they own all cards of a particular company. There is one modifier to this: whatever single card is face-up at the end of the round is the company that went bankrupt, and all matching cards are worth negative points (even if part of a majority). As such, there is often some frantic trading with the center once players perceive that the round is close to ending.
The player that ends the round gets a five-point bonus if their hand consists only of majority or totality shares. They pay a five-point penalty otherwise. This mechanism generally prevents players from just ending the round on a whim, unless they are far enough ahead that they can afford it (in which case, it offers a way for a game to end faster if the winner is essentially determined anyway).
You play a number of rounds equal to the number of players, with highest combined score being declared winner. Overall, it is a fast-moving game that serves well when there is not much time for an extended game, or if you are looking for lighter fare after playing something particularly involved. Be aware that the game often involves lots of frantically-raised voices, so do not play in an area where you would be disturbing anyone else's quiet time.
Oh, and I make absolutely no excuses for the box art. Getting people to look past the eyesore red-and-yellow logo is probably the hardest barrier to entry for this game, and I can offer no suggestions there.