My question is Can I legally stay till Oct 2013.
And My family recently got L2 Visa based on I94 and they are out US currently. Can they travel now to US as they have valid visa which is till Apr 2018.
You need to talk to your employer's immigration lawyer immediately. They should already have advised you what the implications of the L-1 denial are.
If you are still maintaining the L-1B status you may remain in the US and continue to work. However if you are not still in L-1B status you must leave the US as soon as practicable.
Your family members will only be able to use their L-2 visas so long as you are maintaining an L-1 visa. If you are not in status then they are not permitted to use the L-2 visas; the L-2 visas would be invalidated.
If your employer and their lawyer are not providing you with advice and information about your case, you should immediately ask for them in writing to explain your current situation and then take this to an immigration lawyer for it to be reviewed.
Remember, your employer's immigration lawyer is NOT your lawyer. You are just a 3rd party beneficiary of their arrangement. However you are still entitled to an explanation about what your current status and work authorization are.
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