Yeah with Sanskrit you get sentences where the word order if taken directly into English would be something like: "once upon a time, a certain lion, of the cave, in the mountain, he lived" which would mean in more idiomatic English "once upon a time a [certain] lion lived in a mountain cave", or something.
Also it tends to not have more than one finite verb per sentence so fills in the need for other verbs using non-finite verbal forms, so if you very literally translated a sentence you might have something like "The prince, having awoken, having gotten out of bed, having gone to the balcony, saw the bird". The "having x-ed" was the convention we were introduced for understanding the past passive participle (PPP) which is pretty ubiquitous apparently (and has been very common in the extracts we've looked at!), although we were advised that less formally it might be typical to translate them as a past tense verb (e.g. instead of "having gone to the balcony, saw the bird", have "he went to the balcony and saw the bird").
We've not used any texts directly, and only some short adapted passages from a reader developed for teaching Sanskrit. The reader passages are adapted from actual Sanskrit texts though, I gather, although sometimes it's not all that clear exactly what it's from! The texts modules start from second year, alongside the Sanskrit Language 2 (the second year language module). They aren't purely about studying the texts though and also serve as a form of language instruction in of themselves, is I think the design of the Sanskrit curriculum at SOAS.
Although because of the restructuring of degree programmes and the South Asian Studies department, I'm not sure if all of them will be offered again...I expect they might only offer the yoga texts option now, since that corresponds to material taught on the yoga studies MA from which many students on the Sanskrit language modules are drawn. I'm hoping the epic texts module gets offered since that was the one that I was most keen on out of the ones on offer. There is/was epic texts, yoga texts, Hindu texts (although I think these overlap with the epic texts somewhat), court literature and another on poetry (although I think these last two overlap and the particular format depends on whether you're UG or PG; also I think these last two require Sanskrit 2 as a prerequisite, because I guess dealing with poetry and metrical systems and maybe more elaborate (?) court literature is a bit harder and requires more background.
From what I've done of Greek, the word order is usually pretty free. The verb often goes at the end, but not always, and there are some enclitics which can't go first in the sentence, and certain constructions which go in a particular order, but otherwise things aren't that rigid I guess, in theory anyway! However Athenaze (the textbook we were using) which was all passages specifically constructed for language learning, tended to mostly have things in a relatively easy to understand order.
In principle this is also the case with Latin I guess, and Sanskrit, but in practice Sanskrit prose it seems tends towards some structure (but because it's heavily inflected like Greek and Latin you can theoretically just put the words mostly anywhere and usually figure out what the meaning is, so in Sanskrit poetry apparently word order is mainly determined by whatever fits the metre being used).