01 toyota avalon vsc, vsc off, and parking brake light on

OK, because the check engine light is on you need to get this looked at as soon as you can. VSC stands for 'Vehicle Stability Control'. It is a safety system that works through your Brakes so Get It Repaired to be safe driving!!
VSC is designed to help control your vehicle to stop it spinning or sliding out when cornering. Times like driving on icy, rain soaked roads or simply too fast into a corner. This could be anything from a blown fuse, a faulty wheel sensor or even an problem with your actual brakes.

Have the remote checked. Remotes have batteries and will eventually go bad. In the worst case, you may need to buy a new remote and have it programmed.

...

normally located under or beside brake master cylinder

Remove the brake fluid cap which contains the sensor and shake it ,a good arm swing and if its sticking then this will free it it up

faulty abs module.

Toyota Avalon 2006 vsc, skid light and check engine light on. Codes P0031, P0038 and code ,P2238

It takes a special reset tool. VSC (Vehicle Stability Control) it's Toyotas' version of anti lock brakes. One of your sensors are either loose, shorted or disconnected and it needs to reset once scan has been done.

My sister had a RX300 with the same problem,(VSC--ABS ) there is a hose on the back of the air filter housing that has come loose ,it is in a tight spot ,they plugged the hose back up and the lights were not on,I do not know about the alarm,

The crankshaft sensor need to be checked.

You have to use a scanner and pull the code out that is causing the check engine light to come on. whatever code/codes you find are probably related to vsc light.
Good luck and keep me posted