After clearing out my shed I found an old cab I used to use in my old band. I opened up the back and saw it had some old Simms Watts speakers in it. I always used to run this cab with my old Solid State Marshall and I remember the cab always sounded really good. BUT my problem is that there's only one input in the back of the cab and it doesn't state the ohm's.

On the speakers it says the Impedance is 15, but I only have three options on the back of my 5150III, 4,8 and 16. I tried my line 6 pod through the cab and it works, but obviously I want to make 100% sure I know the ohm's of this cab before I run my tube heads through it!
No idea at all. There's no logo's, nothing on it. The only thing I can go by is the Simms Watts speakers inside. It's a really really old cab.
if you have a multimeter you can test the ohmage of the cab by pluggin in a speaker cable to the input and uses the tips of the multimeter on the sleeve and tip of the cable. but if it is 15 ohms, the 16 ohm setting will be fine.
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When you say speaker"s" how many speakers. If it says 15 ohms and is 1 speaker then it would be 15 ohms. But 2 or 4 speakers can be wired various ways to get different ohms. Way to be sure is with an ohm meter. As you used it with a SS amp good chance its 4 or 8 ohms.