As from your comment you use a Raspberry Pi 3 but such a model does not exist. I assume you mean a Raspberry Pi 3B with integrated 10/100 Mbit/s Ethernet, 802.11n wireless, Bluetooth 4.1.
The Raspberry Pi has three interraces: eth0 to the internet router, eth1 to the local DD-WRT router and tun0 (I guess you use the default VPN interface) to the VPN server anywhere on the internet. Problems with more than two interaces are mostly from wrong configured routing. For this setup eth0 and eth1 must have static ip addresses because they are addressed as gateways on routes.
You have three router and four different subnets: the subnet of eth0 to the internet router, the subnet of eth1 to the DD-WRT router, the subnet of the VPN, and the subnet of the ethernet and wifi clients (if they are bridged by the DD-WRT router and both live on the same subnet). It may be possible to also bridge the port on the DD-WRT router to the RasPi (eth1) so the RasPi belongs also to the subnet of the ethernet and wifi clients. That reduces the subnets by one, but it is another configuration and a lot of guess. So I will look at four subnets.
You should have set the default gateway on the DD-WRT router to the ip address from eth1 on the RasPi.
On the RasPi the default gateway must be set to the static ip address of the internet router. I just don't know if this is set by default from the setup. You should check it. To route traffic to the VPN you must set a static route to that network with the ip address of the VPN server as next hop (gateway). To return packages from the internet and from the VPN to your local clients you also must set a static route to their subnet with next hop the ip address of the DD-WRT router. So with the default gateway you have three static routes on the RasPi, one for each interface.
On the internet router you must set a static route to the subnet of the ethernet and wifi clients. Next hop (gateway) of that static route is the ip address of eth0 on the RasPi. If you do not have access to the internet router you can fake it with a NAT (network address translation) on interface eth0.
On the VPN server you must set a static route to the subnet of the ethernet and wifi clients. Next hop (gateway) of that static route is the ip address of tun0 on the RasPi. If you do not have access to the VPN server you can fake it with a NAT on interface tun0.
I hope I haven't overseen something.
I have described a similar but less complex setup at How To Create A Private Subnet Behind Raspberry Pi?. It may give you an idea how it should work.
To reduce complexity you may consider to completely replace the DD-WRT router by the RasPi. With its wifi and ethernet interfaces it can do that.