This is a decent concept, however I do take issue with a few different things: (note that these three spells are all iterations of the same spell, just limited differently)

• The biggest issue I have with the way these are written is that they require you to be using a specific weapon, but further limit you to a specific element based on the weapon you choose. Not every spell has to be elementally agnostic- in fact the elements chosen for a spell take part in how it's balanced and used. However, I don't see any reason why a character using a greatsword shouldn't be able to use the thunder-type spell, or a spear-fighter being able to use the fire-type spell.
• The other big issue I see with these is that the damage values are VERY low for third-level spells. I understand the concerns involved with letting a character make a weapon attack with a potential magic weapon in addition to the damage involved with the spell, but magic items shouldn't be the foundation of the balancing of a spell. Even with the spell that has the best area of effect (a 30-foot cone), doesn't have the range, nor the area of effect to compete with Fireball. The damage is almost one third of that, too. I would've assumed that these spells would've done slightly more damage to the initial target in addition to the AoE, but I don't see that here either. Two of these spells provide slight buffs in addition to the damage, but I don't believe it's quite enough to make up for the lack of damage.

I'll say again that I do like the concept of spells that act as individual martial abilities, however this but one idea for it and I think it can be done a little better!