Hi edwardd0017,
Do all the devices in VLANs 20 and 30 have their default gateways set to 192.168.20.254 and 192.168.30.254, respectively? Can the devices in VLANs 20 and 30 ping each other; i.e. is inter-VLAN routing working?
Also, and as Vivek highlighted, in the original post you say that VLAN10's SVI IP address is 192.168.10.254, then you say in the next paragraph:
"I have connected the ASA to the 3750 by routed interfaces (192.168.1.1) --------- (192.168.1.2) and they are able to ping each other."
And after that in your conflagration, you're configuring the interfaces of the 3750 and the ASA in the 10.10.10.0/24 subnet. So we're not sure which one is the correct one.
Also, (and this is just a technicality) for the connection to be a "routed" interface between the 3750 and the ASA, you need to configure it on the 3750 with the command "no switchport", and then add the IP address directly on the physical port, and not on the SVI. As I mentioned, this is just a technicality in terms of calling the port a "routed" port, however this shouldn't stop your configuration from working, because an SVI should work just as well (theoretically at least).
Furthermore, if you do want the link between the ASA and the 3750 to be a routed interface, then you're better off just applying /30 subnet to the link, and making it a point-to-point link.
Example:
!On the 3750
!
configure terminal
!
interface GigabitEthernetx/x
description Link to ASA
no switchport
ip address 10.10.10.2 255.255.255.252
no shutdown
exit
!
ip route 0.0.0.0 0.0.0.0 10.10.10.1
!
end
Other than that, I'm not familiar with the ASA CLI, but is there a reason why you're specifically assigning the IP address 10.10.10.1 on the VLAN 1 interface of the ASA???
