“Is a Power of Attorney (POA) filed in one state (OH) necessarily valid in another (CA)…and… can the POA legally transfer funds or assets of the rightful owner into their own personal accounts and/or family trusts?”
Question one: Probably. Most states’ laws regarding powers of attorney are similar enough that a POA prepared in one state will probably be valid in another. The institution (such as a bank) may insist on reasonable assurance that the POA is valid, however.
Question two: A person acting under a power of attorney is an agent of the person who gave them the power, and as such is acting in a fiduciary capacity. That means, amongst other things, that the agent has to act in the interest of the principal.
So the answer to your question is that the agent can transfer funds or assets so long as it is in the principal’s interest, but transferring it to his or herself, against the principal’s interest, would be a breach of fiduciary duty. The bank won’t know or stop them, but they would be personally liable.