So, you're only allowed to use weapons made from trees, and if you want to try to kill an attacker who is trying to kill you, you will both be effectively naked. Given such restrictive laws of combat, I will presume that the Hague Conventions on warfare (in particular the 1907 convention) do not apply.
What we have here is a situation where personal weapons will either be melee-style objects or missile weapons, but this does not preclude heavier weapons. Also, while the commandments - and God - enforce the rules against the use of non-wooden weapons in combat, the commandments do not specify that non-wooden objects may not be used to produce the entirely wooden weapons, so long at the tools are not used as weapons themselves, and do not remain as part of the weapons in any detectable amount. This means that aside from combat, we have the full range of modern human technology with which we can prepare our weapons.
Timber may be used to produce spears, clubs and maces, and with lamination using tree-based resins plus heat treatment, may be used to produce cutting blades which, while not as sharp as a metal knife, are sharp enough for use against combatants who must be effectively unarmoured. These weapons may be anointed with tree-based toxins.
Since shields are prohibited, dual-weapon use may be common, with one weapon being used to attack while the other is used to defend. Since the use of each weapon is interchangeable, and each may be used to both attack and defend as opposed to being primarily defensive as in a shield, this should be permissible.
With the application of technology, there are a number of missile weapon systems that can be made using no materials other than those found in trees of varying species, those being bows, crossbows and blowguns.
What may have begun as a simple self-bow could through the ages have evolved into a longbow, a recurved bow and even a modern compound bow. Timber could be laminated using tree-based resins to maximise strength and springiness.
From the bow we can derive the crossbow. The lock mechanism would need to be strong, but could be made using laminated wood, and the bow is just a bow mounted on the stock.
Given that combatants must not wear armour, the blowgun becomes an effective weapon. This is a simple wooden tube through which a sliver of hardwood wrapped in a tree-based fibre can be blown.
All of these missile weapons can be anointed with one - or more - of a number of tree-based toxic substances.
Trees can supply timbers which may be used to build trebuchets and other catapults. The counterweight of a trebuchet may be of the hinged-counterweight type with the counterweight bucket filled with wood, or using tree-derived rubber as an energy store, and being used to propel logs or wooden spheres which may be solid or hollow and filled with a variety of interesting tree-based toxins or tree-derived flammable oils.
The following are tree-derived toxins which may be used to enhance the lethality of the tree-based melee and missile weapons:
Curare, which is a fast-acting arrow poison that may be derived from certain trees.
Cerberin, a poison derived from the Suicide Tree, Cerbera odollam, which if injected should act quite quickly to cause cardiac failure.
The Manchineel tree, Hippomane mancinella, the fruits of which contain Physostigmine.
The Castor Oil Plant, Ricinus communis which in certain conditions may grow as a small tree which fits the required criteria, and which produces Ricin, a potent toxin that kills slowly and painfully.
The Strychnine tree, Strychnos nux-vomica, which produces Strychnine, a toxin producing convulsions which lead to death.
Weapons of Mass Destruction
Ricin and some other toxins are effective as a toxin when powdered and distributed in the air, meaning that they could be used effectively if thrown from a catapult or trebuchet or other aerial source. This would constitute a WMD in that it is the employment of a poison over a large area, intended to affect multiple combatants.
It is certainly not out of the question for a sail-powered ship to be made from timber, and rigged with tree-derived sails and rigging or aerofoils. Ships may carry heavy tree-based weapons, particularly tree-oil-based fire ordinance for use against other warships.
A glider can be made entirely from tree-derived materials, with natural or laminated timber spars and ribs, with tree-based ropes connecting the controls to the control surfaces, and using tree-fibre cloth to cover the airframe.
Gliders may be launched from high places or using natural rubber catapults, and can climb using thermals and dynamic soaring.
Once airborne, a glider can drop tree-based weapons on combatants below, including wooden shot or darts which would be effective against helmetless combatants, or they could distribute powdered tree-derived toxins or tree-oil-based fire weapons. A glider may also carry a tree-derived stored-energy missile weapon similar to a ballista for use against other gliders. It may achieve multiple shots if loaded by non-pilot crew members.
Our gliders may also have a natural-rubber "engine" and a wooden propeller, a thick bundle of rubber strands connected to the propeller and the rear of the aircraft, which is wound tightly prior to launch, and released in the event that a bit of extra thrust is required, providing a few minutes of additional power.
So, as we can see, trees can produce - or be used to produce - all sorts of interesting and deadly things.
This is a little iffy, but combatants may be able to wear camouflage body paint and a camouflage loincloth, as it does not count as a shield, and body paint is technically only a stain on the skin, such as may otherwise be acquired during the course of combat. It is not physical protection, nor does it provide much more modesty than a loincloth.
Is a cell-phone or radio - used in combat for communication only - a weapon? As long as you don't try to physically hit an enemy with it - or hide behind it - you should be safe.
As an extension of the communication angle, if not used to cause an enemy physical harm directly, it may be permissible for combatants to carry optical devices such as binoculars or night-vision gear.