When making a melee attack with inflict wounds, do you use your Strength (or Dexterity, if you're using a finesse weapon), on the attack roll or do you use your Wisdom mod?
I'm playing a rogue/cleric and just wanted to know what I should use, and if I added my Dex for making the melee attack with a short sword (since it's a finesse weapon).
For example, I use inflict wounds and it's a sneak attack. Do I roll 1d6 + 2d6 + 3d10 + dex mod damage, or do I roll 2d6 + 3d10 damage?
It seems like you're a little unclear on the distinction, which is blurring some lines.
Inflict wounds requires you to make a melee spell attack. PHB p. 205 tells us that this will use your spellcasting modifier; WIS for your Clerical spellcasting ability. Basically, it's Cast A Spell (action) requiring an attack roll, not an Attack (action) which substitutes a spell for a weapon.
You can't use sneak attack with inflict wounds.
Sneak Attack's prerequisite is that "the attack must use a finesse or ranged weapon." (PHB p.96) But you didn't use a weapon, you used a spell. So no sneak attack for you. (With this spell--there are others, like booming blade, which trigger off of weapon attacks and so could stack with sneak attack.)
I think you're conflating two different things here.
First, I recommend taking a look at PHB page 192. It starts a list of Actions In Combat. The first one is Attack, and the second is Cast a Spell. Typically you only get to do one of these on your turn.
Attack is what you would do with your short sword, and it is indeed based on your choice of either your strength modifier or your dexterity modifier. As a rogue, you may also qualify for sneak attack damage. Ask your DM if you're unsure.
Cast A Spell is a different action that you would have to use to cast Inflict Wounds. It is listed as a Touch range spell, so it's necessary for your character to physically touch the opponent. The first words in the spell's description are "Make a melee spell attack". Referring to page 205 for those rules, you use your spellcasting ability modifier (Wisdom for clerics) plus your proficiency bonus. No weapons are involved in this attack.
