Nodes in different subnets cannot ping each other

But hosts cannot ping or access the hosts in the other subnets.

have you tried another service (i.e. not icmp)? if it still does not work, you may try tcpdump on bigip to see what the wrong is.

 tcpdump -nni 0.0:nnn -s0 -w /var/tmp/output.pcap host x.x.x.x and host y.y.y.y -v

x.x.x.x is source ip
y.y.y.y is destination ip

None of the hosts can access the internet either.

you have configured default route in bigip, haven't you?