Well whenever anybody tells me their card pool is limited I just to suggest mostly commons, because even if I suggest cards that they don't have, they're probably only 40 cents away from a full player's set of them.
With that said, I would like to pose that typically there are two types of elf decks: Beatdown and Mana-Combo, (Priest of Titania + Fireball is the simplest). This is looking more like a beatdown style - in other words you plan to win by overwhelming your opponent with creatures.
And with THAT said, there are typically two reasons for making a creature theme deck: 1) Fun, (Which, at least at the CPA, is ALWAYS a good reason to do anything) and/or 2) Synergy.
Well the shear act of making and playing the elf deck, no matter how good or bad it performs, should cover the fun side of things. However, you came here for advice, which implies that you want some help with synergy.
Well, these are probably the most synergetic cards for elves:
Priest of Titania
Wellwisher
Wirewood Pride
Coat of Arms
Coat of Arms can be hard to get, as can Priest of Titania, (Even though it's just a common). You might not want to run the Priests anyway; they're great mana speed, but unless you have a place to put all that mana, they'll be dead cards. Beatdown-style elves usually don't need them.
Here is a decklist for a Type 2 elf-beatdown deck I built shortly after Onslaught came out:
Land:
Forest x16
Tranquil Thicket x4
Creatures:
Llanowar Elves x4
Taunting Elf x3
Elvish Archers x4
Elvish Warrior x4
Wirewood Herald x3
Bloodline Shaman x3
Heedless One x4
Krosan Tusker x4
Spells:
Insist x4
Wirewood Pride x4
Overrun x4
I don't imagine you want to just copy somebody else's deck, especially when you probably lack a lot of the cards, but this should give you some ideas. The deck beats down consistently enough. Commons that are in this build which I suggest you use in your deck are Llanowar Elves, Elvish Warriors, Tranquil Thickets, Wirewood Pride, Taunting Elf and, to a lesser extent, Krosan Tusker. Llanowar Elves are good for early acceleration AND offense, as well as for stalling out by blocking. Elvish Warriors are just a quality, quality weenie. Tranquil Thickets are versatile lands, since you likely won't need more than 5 or 6 on the table, you can just draw cards later. Wirewood Pride is a much better way to sneak a lot of damage through than Tribal Unity. Taunting Elves provide one-turn evasion to all of your creatures, which can be enough to win the game, especially if you're packing a Wirewood Pride. Krosan Tuskers may not be your style, and they don't really fit the elf theme, but they are one of the best card-drawing engines green has had in a looooong time. Play them if you want. They might be hard to come by.
If I were you I'd also go out of my way to get Heedless Ones. Trample wins games, trust me.
Cards you have in your list that I think are too weak are:
Elvish Pathcutter: Paying four mana for a 1/2 is way too much unless it does something really good, and this one doesn't. Forestwalk is not worth it. Taunting Elves provide much more consistent evasion.
Wirewood Champion?: I assume you mean Wirewood Channeller. It's a nice card, but you don't really have anything to do with a ton of mana each turn, so it's mostly just an overpriced 2/2. Besides, Priest of Titania is much better acceleration in a mono-green setting.
Awakening: Good card, but you don't really have anything amusing you can do with it. You'll just open yourself up for your opponent to maybe find a way to abuse it.
Elvish Fury: Is a little strange. You'd do better to work on your card drawing and deck thinning before adding overpriced, creature fatteners, (This goes for Giant growth too, but Giant Growth is MUCH better than this).
Tribal Unity: Again, Wirewood Pride will work much better.
Hope this helps.
