Can the laity use exorcised salt? If so, what are the rules for the proper use, handling, and storage of exorcised salt?

The traditional (pre-Vatican II) blessing for holy water in the Rituale Romanum (Roman Ritual) includes exorcisms of salt and water:

_{1. On Sundays, or whenever this blessing takes place, salt and fresh water are prepared in the church or in the sacristy. The priest, vested in surplice and purple stole, says:}

P: Our help is in the name of the Lord.

All: Who made heaven and earth.

2. The exorcism of salt follows:

God's creature, salt, I cast out the demon from you by the living ✠ God, by the true ✠ God, by the holy ✠ God, by God who ordered you to be thrown into the water- spring by Eliseus to heal it of its barrenness. May you be a purified salt, a means of health for those who believe, a medicine for body and soul for all who make use of you. May all evil fancies of the foul fiend, his malice and cunning, be driven afar from the place where you are sprinkled. And let every unclean spirit be repulsed by Him who is coming to judge both the living and the dead and the world by fire.

All: Amen.

Let us pray.

Almighty everlasting God, we humbly appeal to your mercy and goodness to graciously bless ✠ this creature, salt, which you have given for mankind's use. May all who use it find in it a remedy for body and mind. And may everything that it touches or sprinkles be freed from uncleanness and any influence of the evil spirit; through Christ our Lord.

All: Amen.

Exorcism of the water:

God's creature, water, I cast out the demon from you in the name of God ✠ the Father almighty, in the name of Jesus ✠ Christ, His Son, our Lord, and in the power of the Holy ✠ Spirit. May you be a purified water, empowered to drive afar all power of the enemy, in fact, to root out and banish the enemy himself, along with his fallen angels. We ask this through the power of our Lord Jesus Christ, who is coming to judge both the living and the dead and the world by fire.

All: Amen.

Let us pray.

O God, who for man's welfare established the most wonderful mysteries in the substance of water, hearken to our prayer, and pour forth your blessing ✠ on this element now being prepared with various purifying rites. May this creature of yours, when used in your mysteries and endowed with your grace, serve to cast out demons and to banish disease. May everything that this water sprinkles in the homes and gatherings of the faithful be delivered from all that is unclean and hurtful; let no breath of contagion hover there, no taint of corruption; let all the wiles of the lurking enemy come to nothing. By the sprinkling of this water may everything opposed to the safety and peace of the occupants of these homes be banished, so that in calling on your holy name they may know the well-being they desire, and be protected from every peril; through Christ our Lord.

All: Amen.

3. Now the priest pours the salt into the water in the form of a cross, saying:

May this salt and water be mixed together; in the name of the Father, and of the Son, ✠ and of the Holy Spirit.

All: Amen.

P: The Lord be with you.

All: May He also be with you.

Let us pray.

God, source of irresistible might and king of an invincible realm, the ever-glorious conqueror; who restrain the force of the adversary, silencing the uproar of his rage, and valiantly subduing his wickedness; in awe and humility we beg you, Lord, to regard with favor this creature thing of salt and water, to let the light of your kindness shine upon it, and to hallow it with the dew of your mercy; so that wherever it is sprinkled and your holy name is invoked, every assault of the unclean spirit may be baffled, and all dread of the serpent's venom be cast out. To us who entreat your mercy grant that the Holy Spirit may be with us wherever we may be; through Christ our Lord.

All: Amen.

This rubric answers your question:

5. Christ's faithful are permitted to take holy water home with them to sprinkle the sick, their homes, fields, vineyards, and the like. It is recommended too that they put it in fonts in the various rooms, so that they may use it to bless themselves daily and frequently.

Since holy water contains exorcised blessed salt, the faithful are permitted to do the same with blessed salt.

However, salt blessed for the purpose of baptism (baptismal salt) is not to be given to the faithful, according to this rubric from the baptism ritual:

55. … Salt thus blessed [for the exclusive use in a baptism rite] should not be given to anybody, nor even returned to anybody who may have brought it for the blessing, but it should be saved exclusively for baptism or thrown into the sacrarium.