[RPG] Dual wielding two +1 Longswords, do they stack

It really depends. for a cleric, they are functionally identical.

Here are the damage expressions:

Two hander: 2d6 + str

TWF: 1d6 + str, 1d6

Literally exactly the same when you factor in that your to-hit is going to be the exact same number for both. You only get your Divine strike (I think War domain gets that at 8 and 14 like the Life cleric does) on the first hit so that does favor TWF slightly at 8 and more at 14.

The next thing to look at is the action economy. TWF uses your bonus action every round. Whereas GWF leaves it free. You've got some bonus action spells you might want to use.

Lastly, there is feat selection. A melee cleric is MAD (Multiple Ability Dependent) so you might not want to actually pick up a feat and let both your stats run up to 20, but if you could settle for an 18 str, you might want to pick up the feat related to your fighting style. The GWF feat gives you extra attacks, but the TWF feat lets you wield one handed weapons rather than only light weapons and boosts your AC a bit.

Really, looking at the numbers, the decision is entirely up to you and how you want to play the character, they are quite similar. I give the damage edge to TWF, and the action economy edge to GWF. Ultimately though, at high levels, your cantrips might end up doing more damage than your weapon attacks anyways.

You can wield & attack with two weapons without any special class feature or feat.

Like most contests, however, some restrictions may apply. From the PHB, p195 (emphasis mine):

Two-Weapon Fighting
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.

As long as both weapons are light weapons, you can attack with both at the cost of an action for the first attack, as normal, and then a bonus action for the second attack. The second attack does not receive your ability modifier as a bonus to damage the way attacks normally would.

Fighters & some other classes have an option for their Fighting Style class feature which is also called, confusingly, Two-Weapon Fighting. This feature is not required to attack with two weapons as described above; the benefit it gives is to allow you to add your ability modifier to the second attack's damage.

The Dual Wielder feat is likewise not required to attack with two weapons as described above; it instead provides additional benefits and removes other restrictions/penalties when you choose to do so.

Dual Wielder and the Two-Weapon Fighting style make you better at fighting with a weapon in each hand, but are not required to do so.