Appears running:
F   UID   PID  PPID PRI  NI    VSZ   RSS WCHAN  STAT TTY        TIME COMMAND
4     0 26330 26263  20   0   7588   980 -      R+   pts/2     33:52 \_ ethtool -L eth1 combined 3

All that touches it seems to get affected, so e.g. a ltrace/strace get stuck as well.

Meanwhile the log on virsh console of the guest goes towards soft lockups:
[  568.394870] NMI watchdog: BUG: soft lockup - CPU#0 stuck for 22s! [ethtool:26330]
[  575.418868] INFO: rcu_sched self-detected stall on CPU
[  575.419674]  0-...: (14999 ticks this GP) idle=66d/140000000000001/0 softirq=21127/21127 fqs=14994 
[  575.420779]   (t=15000 jiffies g=11093 c=11092 q=9690)

More Info in the journal:
 NMI watchdog: BUG: soft lockup - CPU#0 stuck for 23s! [ethtool:26330]
 Modules linked in: openvswitch nf_defrag_ipv6 nf_conntrack isofs ppdev kvm_intel kvm irqbypass crct10dif_pclmul crc32_pclmul parport_pc parport joydev serio_raw iscsi_tcp libiscsi_tcp libiscsi scsi_transport_iscsi autofs4 btrfs raid10 raid456 async_raid6_recov async_memcpy async_pq async_xor async_tx xor raid6_pq libcrc32c raid1 raid0 multipath linear psmouse aesni_intel aes_x86_64 glue_helper lrw gf128mul ablk_helper cryptd floppy
 CPU: 0 PID: 26330 Comm: ethtool Not tainted 4.4.0-18-generic #34-Ubuntu
 Hardware name: QEMU Standard PC (i440FX + PIIX, 1996), BIOS Ubuntu-1.8.2-1ubuntu1 04/01/2014
 task: ffff8801b747d280 ti: ffff8800ba58c000 task.ti: ffff8800ba58c000
 RIP: 0010:[<ffffffff815f1a43>]  [<ffffffff815f1a43>] virtnet_send_command+0xf3/0x150
 RSP: 0018:ffff8800ba58fb60  EFLAGS: 00000246
 RAX: 0000000000000000 RBX: ffff8800bba62840 RCX: ffff8801b64a9000
 RDX: 000000000000c010 RSI: ffff8800ba58fb64 RDI: ffff8800bba6c400
 RBP: ffff8800ba58fbf8 R08: 0000000000000004 R09: ffff8801b9001b00
 R10: ffff8801b671b080 R11: 0000000000000246 R12: 0000000000000002
 R13: ffff8800ba58fb88 R14: 0000000000000000 R15: 0000000000000004
 FS:  00007fb57d56c700(0000) GS:ffff8801bfc00000(0000) knlGS:0000000000000000
 CS:  0010 DS: 0000 ES: 0000 CR0: 0000000080050033
 CR2: 00007fb57cd7b680 CR3: 00000000ba85a000 CR4: 00000000001406f0
 Stack:
  ffff8800ba58fc28 ffffea0002ee9882 0000000200000940 0000000000000000
  0000000000000000 ffffea0002ee9882 0000000100000942 0000000000000000
  0000000000000000 ffff8800ba58fb68 ffff8800ba58fc10 ffff8800ba58fb88
 Call Trace:
  [<ffffffff815f1d9a>] virtnet_set_queues+0x9a/0x100
  [<ffffffff815f1e52>] virtnet_set_channels+0x52/0xa0
  [<ffffffff8171fc3c>] ethtool_set_channels+0xfc/0x140
  [<ffffffff81720afd>] dev_ethtool+0x40d/0x1d70
  [<ffffffff811cafc5>] ? page_add_file_rmap+0x25/0x60
  [<ffffffff8172f8d5>] ? __rtnl_unlock+0x15/0x20
  [<ffffffff8171ec61>] ? netdev_run_todo+0x61/0x320
  [<ffffffff8118d8a9>] ? unlock_page+0x69/0x70
  [<ffffffff81733b42>] dev_ioctl+0x182/0x580
  [<ffffffff811bf9f4>] ? handle_mm_fault+0xe44/0x1820
  [<ffffffff816fb932>] sock_do_ioctl+0x42/0x50
  [<ffffffff816fbe32>] sock_ioctl+0x1d2/0x290
  [<ffffffff8121ff9f>] do_vfs_ioctl+0x29f/0x490
  [<ffffffff8106b554>] ? __do_page_fault+0x1b4/0x400
  [<ffffffff81220209>] SyS_ioctl+0x79/0x90
  [<ffffffff818243b2>] entry_SYSCALL_64_fastpath+0x16/0x71
 Code: 44 89 e2 4c 89 6c c5 b0 e8 3b dc ec ff 48 8b 7b 08 e8 f2 db ec ff 84 c0 75 11 eb 24 48 8b 7b 08 e8 d3 d6 ec ff 84 c0 75 17 f3 90 <48> 8b 7b 08 48 8d b5 6c ff ff ff e8 4d e0 ec ff 48 85 c0 74 dc

Sometimes there is this on top
 [<ffffffff815f1a53>] ? virtnet_send_command+0x103/0x150

Need to check if there is a loop in virtnet_set_queues that could call virtnet_send_command infinitely.

Being stuck in the kernel explains why signals and traces can't attach.

Note - we are already on todays: 
Linux guest-virtio-dpdk 4.4.0-18-generic #34-Ubuntu SMP Wed Apr 6 14:01:02 UTC 2016 x86_64 x86_64 x86_64 GNU/Linux

I seem to be able to work on old ssh sessions, but new sessions get stuck as well - need to prepare more next time :-)

Next Steps:
 - analyze code pointed out by hangs