Archaic Roman religion is very much similar to Shinto, though their origins and the details are obviously very different. Rome's religious system in all pre-Christian periods rested more or less on a system of numina ("spirits" or "powers") tied to ritual, physical space and meta-domain. It is thought that early Roman religion was very much like early Celtic religion, though getting at either of them now, given the very limited evidence, is a tough road. What Caesar tells us (in Bk VI of BG) seems like the attempt to map a largely aniconic system onto a more familiar iconic one. Books on this subject tend to be in very dense, difficult French or German and are a little beyond my understanding. And incidentally, neither Archaic Roman nor early Celtic religious practice maps very well onto what we can gather about an early "Indo-European" religion, which seems much more akin to myth-making systems of the Near East and Greece.

Overlaying this "animism" substrate was the developed Hellenistic mytho-hierarchy of the Olympian gods and the thousands of minor deities within the web of myths surrounding those gods, slowly borrowed or in some cases imported wholesale from the cultures with which Rome came into contact and ultimately absorbed, beginning with a sort of second-hand version from their Etruscan neighbors, then the cities of Magna Graecia of central and southern Italy. This is the most familiar aspect of "Roman gods," as they generally map well onto the well-known Greek gods. The Etruscan intermediary for some of the very earliest "Greek" ideas, having been imported into Etruria during the 8th-6th centuries BCE via Phoenician and Greek colonials, along with the elusive early "animist" Roman substrate, produced a very complicated and entangled "Roman Religion" by the time of the Late Republic. The Etruscans, not being Indo-Europeans, were unlike any other culture in the Mediterranean in the Iron Age, with some bizarre and fascinating religious aspects. They are super weird, in short, and their weirdness leaked out into Roman practice. Not even the Romans themselves knew why they themselves performed some rituals, or what they meant, or from what origins. And, as if that picture wasn't opaque enough, we then have Christian Romans muddying the waters further in Late Antiquity, writing their (often, not always) misguided musings about "Roman Religion" half a millennium later through a Christian lens.

The book to go to here is still Dumezil, which I wrote a bit about over here.