Hm, interesting. I started with adding ping to st0.0's host-inbound-traffic system-services on both routers as you suggested. I can ping 172.19.19.1 from 172.19.19.120 and vice versa, so the VPN seems to be fine.
So, on the SRX240 I continued with replacing:
route 10.120.0.0/16 next-hop st0.0;
with
route 10.120.0.0/16 next-hop 172.19.19.120;
With this in place, I can ping anything on the network behind the SRX210 from the SRX240.
However, pinging the SRX240 internal interface (the int zone, 10.101.13.15) from the SRX210 does not work. So I did the same thing on the SRX210, I replaced:
route 10.101.0.0/16 next-hop st0.0
with
route 10.101.0.0/16 next-hop 172.19.19.1;
But that didn't work. I still cannot ping the interface in the int zone on the SRX240 from the SRX210.
Any ideas?