You are covering a couple fairly wide topics with your question.
Concerning VLANs: VLANs are (by Cisco's definition) broadcast domains ... as if they were a single segment of virtual wire connecting each of the participating devices. VLANs are a Layer Two vehicle ... If you had a switch (L2 variety) with two (or more) VLANs defined, the VLANs would not be able to talk to each other, even if they are in the same container/chassis, unless you introduce a Layer Three device (Router or Layer Three switch). Each VLAN is treated as a separate chunk of cable ...
Regarding routable / non-routable protocols:
"Routable" implies a Layer Three device. "Routes" equate to individual segments, each of either a different "network number," and possibly media type (Token-Ring, Ethernet, Serial, ...).
In order to be routable, a protocol must provide space to address the individual segments. A frequent analogy would be a street address.
If a letter was only addressed to "1546" (no street, city, state, zip) the post office wouldn't have any idea of where "1546" is (so it tosses the mail in teh "dead letter" pile where it rightfully rots until disposal.
If the adddress was "1546 Main Street,"(no city, state, zip) then the post office could assume it was local, especially if they knew that Main Street had an address range including "1546" as one of their addresses.
If the address was "1546 Main Street, Anytown" then the post office could forward that letter to the post office in Anytown, and let them worry about if there's a "1546 Main Street." When the Anytown PO gets the letter, they can deliver it because they know exactly where 1546 Main Street is.
With a complete address, the letter can be routed with near-certainty that it will arrive where it was supposed to go.
Now with that all being said; a Layer Two protocol (like Ethernet) has no place in the header for an address beyond the local segment ("chunk of wire, virtual or real") ...
The Layer Three protocol (Like IP) has a defined method for explicitly addressing segments, and a place in the protocol header to put the "network address" (the more explicit address, like adding a city, state zip on a letter). Some Layer Three protocols are IP, IPX, DecNet, AppleTalk (and many more, living and dead).
By using a Layer Three protocol, you are providing an addressing system where a local device can forward the encapsulated data to a remote segment hop-by-hop .... where each hop is one step closer to the ultimate destination ("Anytown"). When the encapsulated data reached the final device, it knows the Local addres (the Layer Two address - "1546 Main Street") and send the data specifically to that Local address.
Finally, OSPF and RIP (along with EIGRP, IGRP, BGP, IS-IS ...) are routing protocols. They can dynamically determine the best (layer three) path from "this device" to the (remote / non-local) destination. Sort of like the morning traffic report ("This street is blocked by an accident, try this other road").
Without dynamic routing protocols, every path would have to be manually mapped ... from every "Point A" to every other "Point B" that existed within the universe of devices that you would want the originating device to talk to .... a seriously ugly administrative task.
SO, the short story:
VLANs are a layer two thing (no off-LAN addressing)
A routable protocol must have, and be able to utilize, an off-LAN "network address" or networking portion of the address.
Routing (versus "routable" as above) protocols provide the roadmap (routing table) of "how to get data from here to there" (where "there" is remote to the local segment - which may or may not be a VLAN).
Standard Disclaimer: Some information may be (slightly) bent, folded, spindled, or mutilated for the sake of brevity and (hopefully) clarity.
FWIW
Scott
