Who has rights to my late husband's things?

Sorry to hear about your husband.

Since your husband did not leave a Will, the rules of intestate succession determine inheritance.  Intestate means dying without a Will. 

Under intestate succession, you, the surviving spouse would inherit your husband's entire estate including the items your stepsons have illegally removed from the cabin.  You could sue your stepsons for trespass and trespass to chattel or  conversion.  Trespass is the volitional entry onto the land of another without consent or legal privilege.  This would apply to entering the cabin without your consent.  Trespass to chattel is the intentional taking or damaging of the personal property of another without consent or legal privilege.  Conversion is the intentional assumption of dominion and control over the personal property of another.  Conversion is applicable if your stepsons are asserting ownership of the personal property they removed from the cabin to the exclusion of your rights as owner.  Conversion is an unauthorized act which deprives you, the owner of your property permanently or for an indefinite time. 

If your stepsons took the items and are going to keep them permanently or for an indefinite time, your lawsuit would be for conversion instead of trespass to chattels.  Your damages (the amount of compensation you are seeking in your lawsuit) for conversion would be forced sale which is the replacement cost of the items.

You would file one lawsuit naming your stepsons as defendants.  Your lawsuit would have the following separate causes of action (claims): trespass and conversion.  If the items are returned after a short period of time, then your cause of action would be for trespass to chattels instead of conversion.