I just got a job offer with a mobile entertainment network company. But it doesn't feel right with what they are asking. They want my account information. But they also want my user name and password to my account. I never had a job ask that before. Should I back away?
Scam. They have absolutely no justification for requesting your password.
Don't back away. Run! And report them to the service they contacted you through, so they can be kicked off it. And to the appropriate government offices; in the US, information about that can be found at https://www.usa.gov/stop-scams-frauds
(The FTC in particular has been going after scam artists fairly actively in the past year. I still wish they could be funded well enough to do that properly, but it helps.)
The only thing even remotely close to this that I have ever seen is getting clearance on a government or military project/sub contractor, and they don't ask for your password (or account name). They may ask you to print out a statement, or to have the bank fill out a form (that would contain account balances and average transaction sizes), but I have never seen, even in that case, a request for a username and password.
This is an obvious scam. Even if your setting up direct deposit (some employers do require direct deposit these days) they only ask for routing numbers and account numbers.
I know of no (and there is no) legitimate use or need for a bank logon and password.
An employer can legitimately make use of a bank account number for direct deposit; and I have heard directly from one employee that their employer requires a bank account for payments; but employers set that up without your bank logon and password.
I would give them fake data and record them while they are asking and taking your account.
Then I would head on the next police station and use the recording as an evidence to send them to jail.
And for people into legalese, see 2nd U.S. Circuit Court of Appeals.