When someone tries to persuade you of the truth of something they said and they use the argument that it is too strange to be made up (or any variations of this, such as "too complicated to be fiction"), is that person making an appeal to your logical reasoning (logos) or to your emotions (pathos)?
This is an appeal to Bayesian statistics. The speaker cannot possibly mean that it is logically impossible for someone to make up whatever-it-is, so they must be meaning that it's extremely improbable. Thus, what they are saying is, effectively, when you are computing the chance of various models given the data, make sure you weight your prior for the "made it up" case appropriately (i.e. very low). Given that, a priori, it's very unlikely that anyone made that thing up, other explanations (even very improbable ones) begin to look correspondingly more favorable.
So it's entirely valid logically (albeit indirect via statistics).
However, although it's potentially valid when doing statistical reasoning, it's not necessarily the case that people intend for you (or themselves) to do it that way. People could be hoping that you will have the same emotional reaction they did: "OMG! No way!!" and then set the a priori probability to zero and thus promote some other perhaps-even-more-wildly-unlikely scenario to be the "best explanation". The correct thing to do may be to recognize that although it's unlikely that someone could come up with such things, everything else is even more unlikely, and thus it-was-made-up is the best explanation (given available evidence).
I'm not sure that a scenario this complicated is well captured by the terms logos, pathos, or ethos. It is like ethos in that arguments from ethos are also arguments about weighting a priori probabilities in a Bayesian framework, but there is no trustworthiness involved here. (Trust is one reason you might adjust your priors.) Although there is logically sound information contained in such an argument, it is usually presented in a very different form than typical appeals to the intellect. Almost no-one is consciously aware of their distribution of prior probabilities, so a more intuitive presentation tends to be more effective (though this says nothing about the validity...).
I don't think it's either an appeal to logos or pathos, but rather an appeal to ethos.
Here's a quick overview of the three classic types of argumentative appeals:
Logos: an appeal to the facts and logic used to support a claim (both inductive and deductive)
Ethos: an appeal to the credibility of the source, including the speaker or author
Pathos: an appeal to the emotions and/or individual motivations of the listener, particularly characterized by the use of vivid language with lots of sensory details
The justification that an argument is true because it is "too strange to be made up" definitely sounds like an appeal to the credibility of the speaker. It sounds to me like you're saying "regardless of whether or not you think I'm a liar, I couldn't have possibly made this one up!"
It's not a particularly strong or convincing argument, mind you, but I think it is clearly an appeal to the ethos of the speaker rather than an appeal to the inherent logic of the argument or an attempt to invoke strong emotions on the part of the listener.
I think this would be an example of a fallacy known as a Red Herring.
A Red Herring is a fallacy in which an irrelevant topic is presented in order to divert attention from the original issue. The basic idea is to "win" an argument by leading attention away from the argument and to another topic.
That the argument is complicated is irrelevant to the truth of the argument.