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I have configured Stretch networking for eth0 (it picked ens3), after setting:

GRUB_CMDLINE_LINUX="net.ifnames=0 biosdevname=0"

grub-mkconfig -o /boot/grub/grub.cfg

reboot

so now I have:

>: cat /etc/network/interfaces

source /etc/network/interfaces.d/*



# The loopback network interface

auto lo

iface lo inet loopback



# The primary network interface

allow-hotplug eth0

iface eth0 inet static

    address 192.168.1.10/24

    gateway 192.168.1.1

    # dns-* options are implemented by the resolvconf package, if installed

    dns-nameservers 8.8.8.8

which works, so:

>: ip a

1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1

    link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00

    inet 127.0.0.1/8 scope host lo

      valid_lft forever preferred_lft forever

    inet6 ::1/128 scope host

      valid_lft forever preferred_lft forever

2: eth0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc pfifo_fast state UP group default qlen 1000

    link/ether 52:54:00:0a:f7:bc brd ff:ff:ff:ff:ff:ff

    inet 192.168.1.10/24 brd 192.168.1.255 scope global eth0

       valid_lft forever preferred_lft forever

    inet6 fe80::5054:ff:fe0a:f7bc/64 scope link

       valid_lft forever preferred_lft forever

And I can ping google nameservers like:

>: ping 8.8.8.8

PING 8.8.8.8 (8.8.8.8) 56(84) bytes of data.

64 bytes from 8.8.8.8: icmp_seq=1 ttl=55 time=10.9 ms

64 bytes from 8.8.8.8: icmp_seq=2 ttl=55 time=10.9 ms

But not google itself, or any other domain. My hosts file looks like:

>: cat /etc/hosts

127.0.0.1   localhost

192.168.1.10    someserver.name.com someserver



# The following lines are desirable for IPv6 capable hosts

::1     localhost ip6-localhost ip6-loopback

ff02::1 ip6-allnodes

ff02::2 ip6-allrouters

My resolv.conf looks like:

>: cat /etc/resolv.conf

nameserver 8.8.8.8

but I can ping my gateway so the default route seems okay:

>: ip r

default via 192.168.1.1 dev eth0 onlink

192.168.1.0/24 dev eth0 proto kernel scope link src 192.168.1.10

my /etc/nsswitch.conf says:

hosts:          files dns

networks:       files

What is missing? Should I be doing something else in Stretch?

It sounds like you may be confusing two issues routing and DNS.
If you are able to ping numerical addresses, like <8.8.8.8> or <128.171.224.100> (www.hawaii.edu) then the issue is DNS, not routing.

The /etc/nsswitch.conf file specifies where to look for DNS information, and in what order to make the queries. Look for the line strating with 'hosts'.

# The primary network interface

allow-hotplug eth0

iface eth0 inet static

    address 192.168.1.10/24

    gateway 192.168.1.1

    # dns-* options are implemented by the resolvconf package, if installed

    dns-nameservers 8.8.8.8

Remove the /24.
Reasons for this:
Syntax wise you're incorrect.

Assuming your 192.168.1.10 address contains a DNS server, removing the /24 should fix your error.