If an ally summons a spiritual weapon, would you be able to grab it and attack with it? And if so, what would the damage and modifiers be?
No; the spiritual weapon is used by the caster
The text in the spell description is pretty clear on who makes the weapon attack: you (the spell caster). It is also clear on who causes it to move.
When you cast the spell, you can make a melee spell attack against a creature ... on a hit, the target takes force damage equal to 1d8 plus your spell casting bonus ... as a bonus action, on your turn, you can move the weapon up to 20 feet ....(PHB p. 278)
What happens when the spell is cast is that it creates a magical effect. If someone else were able to use this weapon as you suggest in your question, they would be making a melee weapon attack, or a melee attack, not a melee spell attack. (Melee attack, PHB p. 195; spell attack rolls, PHB. p. 205).
Why is it important that this spell specifies a melee spell attack? Attacks that are ranged (as opposed to melee) have disadvantage on when opponents are within 5 feet of you. (PHB. p. 195 & p. 205).
A spell is a discrete magical effect. (PHB, p. 201)
As another clue to the spell's function, the spell is described as being from the evocation school, rather than conjuration school. Were a weapon to be created or summoned by this spell, it would most likely have been classified as conjuration.
Some conjuration spells create objects or effects out of nothing (PHB p. 203, side bar, Schools of Magic)
Spells in this edition generally do what is in the spell text. If this magical effect created a weapon that was transferable to another creature, that would be mentioned in the spell's text.
Compare this to a different spell, like Goodberry
Up to ten berries appear in your hand and are infused with magic for the duration. A creature can use its action to eat one berry (PHB, p. 246)
In this case, a creature indicates that use of the berries is not restricted to whomever cast the spell.
For another example, see Magic Stone
You touch one to three pebbles and imbue them with magic. You or someone else can make a ranged spell attack with one of the pebbles by throwing it or hurling it with a sling. (XGtE, p. 160; EE Player Guide, p. 20).
If the unofficial rulings from J. Crawford are of interest, he says this:
A pact weapon is a physical object that someone else can pick up. A spiritual weapon is a spell effect.
No, you can't
If the spell created a usable weapon, the spell's description would say so. It does not.