Trying to troubleshoot an inherited enterprise environment with a Cisco Backbone

I was wondering if someone could help educate me here. Mods if this is against the rules feel free to remove.

My understanding of VLANs is that they cannot communicate between each other unless there is some layer 3 routing between them. I am working in an environment where we have several layer 2 switches connected back to one layer 3 core switch.

The vlans on the core switch are as follows:

interface Vlan1

description ***** DATA *****

ip address 192.168.10.1 255.255.254.0

no ip proxy-arp

!

interface Vlan10

description ***** VOICE *****

ip address 192.168.42.1 255.255.255.0

ip access-group DENY-VOICE-SECURITY out

no ip proxy-arp

!

interface Vlan20

description ***** SECURITY *****

ip address 192.168.0.1 255.255.255.0

ip access-group DENY-VOICE-SECURITY out

no ip proxy-arp

!

interface Vlan22

description **** GUEST ****

ip address 192.168.22.1 255.255.254.0

!

interface Vlan100

description ***** ASA-UNTANGLE *****

ip address 192.168.100.1 255.255.255.248

ip access-group DENY-UNTANGLE-ASA out

no ip proxy-arp

​

Everything is trunked back to the main switch which then goes to an Untangle firewall. Everything is currently running on VLAN 1 apart from the IP phones

What I am confused by:

1.) If I put a switch port on vlan access mode 22 ie:

interface 0/40

vlan pvid 22

vlan participation exclude 1,10,20

vlan participation include 22

exit

and connect a computer to it with a static IP in the 192.168.22.1/23 subnet I cannot get internet access or even ping the 192.168.22.1 gateway. Shouldn't I be able to ping the vlan interface?

I'm not even sure if I am asking the right questions but I hope someone here can put me on the right track.