I'm a big fan of Zombies. I've had a zombie deck of some sort or another ever since Ice Age. I've got a handful of suggestions for this deck, though.
Unholy Strength isn't terrible and it's certainly easy to acquire and cheap to cast. However, I think that you'll typically find there are better ways to pump your creatures. Bonesplitter is the first that comes to mind. It has a bit greater synergy with Skullclamp and doesn't scream "card disadvantage" like Unholy Strength does. A bit harder to acquire, but extremely strong in a deck like this, would be Bad Moon.
I'm not sure I like Festering Goblin in this deck. If you're using him for board control, I suppose he's fine, but he's not a tremendous aggro creature. If you're throwing caution to the wind, anyhow, Wretched Anurid or Blind Creeper might serve you better. They both cost {1}{B}, which looks like it's a bit steep for your mana curve (^_~) but they're really powerful beat sticks. I like Maggot Carrier more, but the same advice might go for them, as well.
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While I'm here, I'd like to share my Zombie deck and get a bit of advice on it. In its present incarnation, this deck is Peasant Magic legal (ie: zero rares, no more than five uncommons) and is my preferred deck for multiplayer games. At present I am using none of my uncommon slots, although I have some ideas for cards that would fit. I'd appreciate some advice concerning what I might remove. There is also the possibility of having a pseudo-sideboard to which I resort before games. If it's a single-player match, use one set of cards, if a multi-player match, a different set.
Creatures (28)
4 Maggot Carrier
4 Carnophage
4 Blind Creeper
4 Wretched Anurid
4 Shepherd of Rot
4 Vengeful Dead
4 Gempalm Polluter
Spells (12)
4 Dark Ritual
4 Vicious Hunger
4 Syphon Soul
Land (20)
20 Swamp
The goal of this deck is to deal damage to its opponent(s) just a little bit faster than it deals damage to itself. Quick, aggressive creatures, like Carnophage, Blind Creeper, and Wretched Anurid are the foundation of the deck.
On their shoulders rest Sheperd of Rot and Gempalm Polluter. Although with an offense such as I am capable of bringing to bear this deck seldom stalls, the ability to deal massive damage without engaging in combat is invaluable. Particularly in multi-player games, Shepherd of Rot is the all-star of the deck. Gempalm Polluter is not the best card, by a long shot, but even a life loss of 2 is worthwhile, since it also draws me a card.
Maggot Carrier is present mostly to fill out the lower registers of my mana curve. With his ability, he fits well into the deck and that one life occasionally makes a difference.
Vengeful Dead is an interesting card. I definitely find him more useful in multi-player than I do in single-player. In single-player matches, I suspect that I would do much better with Undead Warchief (a card I'd forgotten about until I read Exaulted Leader's deck list.) and/or Cabal Interrogator. Having a mixture of 3 Warchief and 2 Interrogator would fill up my uncommon slots for Peasant Magic and would suit me better in a one-on-one match, I think. I'll discuss later what I think I'd swap out, when playing single-player. In multiplayer, at least two members of my group insist on packing multiple Wrath of God/Akroma's Vengeance. In this situation, Vengeful Dead becomes one of my best cards. I don't have to be quite as concerned about overextending myself, since I can feel confident that a Wrath will cause each of my opponents to lose a hefty chunk of life.
Vicious Hunger is my token nod toward board control. This deck typically tries to win before any of my opponents' big threats can hit the table, so I seldom have to concern myself with creatures with toughness greater than 2. The life gain is also very nice, since it offsets this deck's symmetrical tendencies.
Syphon Soul is clearly more useful in multiplayer than it is in single-player. However, the life offset is often useful. In single player, I'd probably opt for Brush with Death over this.
Summary:
Multi-Player
no changes
Single-Player
-4 Vengeful Dead
-4 Syphon Soul
+3 Undead Warchief
+2 Cabal Interrogator
+3 Brush with Death