No matter how much you prep, you will face some arguments that you haven't prepped out. (Depending on your laziness, this may happen more often than not.) In these cases,
When facing squirrely arguments, you may feel like panicking, since you're not at all prepared to deal with them. Here are some strategies that really apply to weird or improbable arguments.
I recommend calling a lot of their link evidence, especially ones that sound too good to be true. This achieves several things. First, you can often find mistakes in their evidence. Ask to see the original source or PDF, as in other parts of the text you can often find contradictions or arguments that support your side. In many cases, to support these squirrely arguments, teams flat-out misconstrue evidence, which can be called out by calling cards. Second, as they look for their evidence, you shouldn't prep, but the second speaker should use that time to think of responses to their case, especially since you likely don't have evidence against it. Finally, in many cases, you might not fully understand their argument after they read their case, and reading their evidence for yourself can help you comprehend what they're arguing in the first place.
Many arguments that sound squirrely have at least one internal link that you likely have responses to. Look for links that they may rush through, or arguments that seem to fit the motif of a similar argument. In most cases, the argument won't be explicitly based on that argument, but as it relies on similar principles, your evidence can be applied to those. For example, an argument that ending arms sales to Saudi Arabia makes them develop chemical weapons to feel safe can be answered with (reasonably stock) responses that Saudi Arabia's security is still assured.
This applies mostly to the first speaker. In first cross, you should highlight the absurdity of their argument through your questions. Many squirrely arguments are based in really improbable links or premises that sound absurd. You can easily take these apart by making their links sound less important than they really are (to set up your partner's link weighing) or to question if the argument is as big a deal as they say it is. Judges are usually implicitly biased against these arguments, as they just sound outlandish - confirm the judge's biases by highlighting how bad the argument is.
As mentioned in the narrative basics article, you should be using your narrative to attack their causality and solvency. Squirrely links are squirrely because they are probably not the most effectual or significant link into their impacts, which makes it much easier for you to weigh your links against theirs. Additionally, they're likely hard-pressed to find solid evidence articulating their entire argument, which is a big indicator that it's not that serious of an issue. Remember the importance of controlling the narrative, as with these squirrely arguments your opponents may try to shift the round to center around them, to throw you off and focus the judge. Applying your arguments to theirs can reinforce the importance of your side.
As with every skill, you only get better with practice. I recommend watching old rounds on Youtube, on topics you didn't debate. For first speakers, watch the case and write down problems you see with it, or questions you'd ask to expose those problems. For second speakers, prep a rebuttal with no evidence against the arguments you watch. For more specific practice, you can watch rounds on topics you did debate, so you know the stock arguments, and find cases that are non-stock to respond to. Deliver a rebuttal, record it, and compare your responses to the second speaker in the video.