Just to be clear, it looks like you’ve listed “all the Completes minus psionic, mage, and champion.” If this is incorrect, please say so.
This type of build will usually be a primarily melee combatant, using spells to become better at that role. For that reason, Evocation should be one of your last choices for a school to specialize in. For this type of character I wouldn’t specialize in any school of magic at all. I understand that you’ve recognized that your party is lacking in both primary arcane magic and melee damage, but one character shouldn’t be expected to fill both of those roles and be good at both. My advice would be to choose one of those two roles to focus on, and taking the other as a secondary role.
In either case, your level build needs some serious work. You’re not observing the optimal ‘jumping off’ levels of your classes. Leading into Spellsword you should have either Fighter 1/ Wizard 6, or Fighter 2/ Wizard 4. The 5th Wizard level grants no BAB or base save bonuses, so stopping at that level is not a good choice for a build which doesn’t want to lose out on BAB or spellcasting. Spellsword itself should be taken for one, three, or five levels. You don’t want to lose out on spellcasting if it can be avoided, and Channel Spell probably isn’t worth waiting another level for your next higher level of spells, or if it is worth taking then you need to make sure you’re not losing out on much spellcasting besides that. Personally, I haven’t seen a build I like yet that uses more than three Spellsword levels, the loss of spellcasting just isn’t worth it.
If you’re going to be focusing on melee, you need to be sure your BAB and spellcasting ability are both as high as possible, and your spells are going to be used to enhance your melee capabilities. Buffing spells along with the feat Arcane Strike (CW) make this kind of character the most capable melee damage dealer in the game. Starting at 7th level, I’d suggest going something like Fighter 2/ Wizard 4/ Spellsword 1/ EK, in which case you could start out with a magical Mithril Shirt without having to worry about arcane spell failure. Wield a two-handed weapon with reach and wear armor spikes, take Power Attack, Cleave, Practiced Spellcaster, Combat Reflexes, and Extend Spell, and gain Leap Attack at EK1 and Arcane Strike at level 9. Another good feat to include early on would be Craft Magic Arms and Armor, in which case you’d be able to start out with some of your most expensive equipment at half price, and you could upgrade what equipment you have however you want to. Don’t worry about casting spells offensively, focus on your physical ability scores and only make your Int high enough to cast your higher-level spells later on.
For a primary spellcaster build, maybe focus on summoning to add melee combatants to the fight, especially considering the PHB2’s Immediate Magic variant for a specialist Conjurer. Conjuration is the most versatile of all the schools, and with the Spell Compendium it gets a fair share of blasting spells as well. Another idea would be to take Improved Familiar and buff it up for melee combat at the start of a fight before switching to offensive spells. In either case you wouldn’t need to worry about your own character’s melee capabilities, so you’d be free to focus on being a better spellcaster.