Vlan's are a switch thing.
Clients and servers dont need to be aware what vlan's they are in.
They only need to be aware of the subnets.
There are some exceptions like hypervisors that apply virtual bridges etc for their guests/VM's that need to be in vlan trunks.
I could be wrong missing some bits but am sure someone here will correct me 
To prevent having to route traffic between the subnets, you could assign all appropriate vlan's to the switch/router port that Pi-hole is connected to.
And create a bunch of aliased IP's for each vlan on one and the same physical connected interface.
Below how is done for Raspbian/Debian using dhcpcd5 network manager (without having to translate that Dutch link):
pi@ph5:~ $ ip -br link show
lo UNKNOWN 00:00:00:00:00:00 <LOOPBACK,UP,LOWER_UP>
eth0 UP b8:27:eb:xx:xx:xx <BROADCAST,MULTICAST,UP,LOWER_UP>
pi@ph5:~ $ ip -br -4 address show
lo UNKNOWN 127.0.0.1/8
eth0 UP 10.0.0.4/24
pi@ph5:~ $ sudo nano /etc/network/interfaces
# interfaces(5) file used by ifup(8) and ifdown(8)
# Please note that this file is written to be used with dhcpcd
# For static IP, consult /etc/dhcpcd.conf and 'man dhcpcd.conf'
# Include files from /etc/network/interfaces.d:
source-directory /etc/network/interfaces.d
auto eth0.0
iface eth0.0 inet manual
auto eth0.1
iface eth0.1 inet manual
auto eth0.22
iface eth0.22 inet manual
pi@ph5:~ $ sudo service networking restart
pi@ph5:~ $
pi@ph5:~ $ ip -br l
lo UNKNOWN 00:00:00:00:00:00 <LOOPBACK,UP,LOWER_UP>
eth0 UP b8:27:eb:xx:xx:xx <BROADCAST,MULTICAST,UP,LOWER_UP>
eth0.0@eth0 UP b8:27:eb:xx:xx:xx <BROADCAST,MULTICAST,UP,LOWER_UP>
eth0.1@eth0 UP b8:27:eb:xx:xx:xx <BROADCAST,MULTICAST,UP,LOWER_UP>
eth0.22@eth0 UP b8:27:eb:xx:xx:xx <BROADCAST,MULTICAST,UP,LOWER_UP>
pi@ph5:~ $ sudo nano /etc/dhcpcd.conf
[..]
interface eth0
static ip_address=10.0.0.4/24
static routers=10.0.0.1
static domain_name_servers=10.0.0.1
interface eth0.0
static ip_address=10.10.10.10/24
interface eth0.1
static ip_address=172.16.0.2/24
interface eth0.22
static ip_address=192.168.0.2/24
pi@ph5:~ $ sudo service dhcpcd restart
pi@ph5:~ $
pi@ph5:~ $ ip -br -4 a
lo UNKNOWN 127.0.0.1/8
eth0 UP 10.0.0.4/24
eth0.0@eth0 UP 10.10.10.10/24
eth0.1@eth0 UP 172.16.0.2/24
eth0.22@eth0 UP 192.168.0.2/24
pi@ph5:~ $ ip -br -4 r
default via 10.0.0.1 dev eth0 src 10.0.0.4 metric 202
10.0.0.0/24 dev eth0 proto dhcp scope link src 10.0.0.4 metric 202
10.10.10.0/24 dev eth0.0 proto dhcp scope link src 10.10.10.10 metric 206
172.16.0.0/24 dev eth0.1 proto dhcp scope link src 172.16.0.2 metric 207
192.168.0.0/24 dev eth0.22 proto dhcp scope link src 192.168.0.2 metric 208
And make sure Pi-hole is set to "Listen on all interfaces" below:
http://pi.hole/admin/settings.php?tab=dns
EDIT: added routes