What follows is my opinion, backed by my personal experiences. Since you're asking.
I do not feel that a person can be both Wiccan and Asatru. Every Wiccatru I've known over the past 17 years has been a complete flake. 100% of them.
There are a number of inherent problems with trying to be both.
1: Focus.
Face it. The focus of Wicca is based in Witchcraft. Magic (I don't and won't spell it with a k... screw you guys). The focus of Asatru is based on the relationship between humanity and the Gods. Dividing that focus will end up making you less of both. Asatru means True to the Gods (Aesir and Vanir).
2: Theism.
Asatru is a hard polytheistic faith. The Gods are the Gods. They're not Jungian archetypes for aspects of nature. They're not aspects of other deities. Thor isn't Zeus, Osiris, and Lugh... The Gods and Goddesses are unique individuals unto themselves. Not parts of a plural set of meta-deities, nor aspects of a singular omnipotent meta-deity.
3: Worldview.
Wicca is a very peaceful religion. Asatru is not necessarily a peaceful religion. Peace is always preferred, but we honor the ability, capacity, and willingness to protect and defend oneself, ones family, one's kin, one's kith, one's homestead, one's community, and one's nation. There is a reason the symbol for Wicca is a harmonious blend of the elements into a living whole, while the symbol for Asatru is the weapon Thor uses to aggressively protect and defend his kith, kin, and community.
4: Wiccan Rede - Havamal. 'nuff said.
I'd say you should be Wiccan.
Why?
It's what you are in your heart.
This means that honestly, you'd end up paying lip service to the Aesir and Vanir.
I won't be arrogant enough to speak for the Gods, but I can't believe they'd care for that.
Compare it thus...
You're married.
Your spouse lives, cohabitates, loves, and has sex with another person. But, once a week, like clockwork, your spouse comes by and says they love you. Then they go back to their life with the person they truly love, and to whom they are truly dedicated.
Personally... *I* would be offended.
I, however, am not one of the Aesir or Vanir. But we get our aptitudes from somewhere.
So... be a Wiccan. Be a good Wiccan. Study, and shape your environment to suit your will, and do so in peace and harmony.
Leave the honoring of the Aesir and Vanir to those who are more suited to such a purpose.
I hope you don't think this is elitist, though you may actually see it that way, I admit. My point is that while you're Wiccan, and that's fine and good... a Wiccan is not an Asatruar.
I'm an Asatruar... and as an Asatruar, I'm not cut out to be a Wiccan. The worldviews are nearly diametrically opposed. Which isn't to say we can't co-exist in peace and relative harmony, but merging the two... doesn't really work.
A poster, above, said our ancestors merged religions... some did... during conversion eras, but they always eventually ended up choosing -A- path. Asatru is not a dabbler religion.
EDIT:
Hahah!
Notice, even when I preface this answer with the fact that it is my opinion backed by my personal experiences, I'm accused of lying, and being dishonorable for stating my opinions.
Priceless. I love fluffies.

I honestly do. (really... no sarcasm or anything, there... fluffies entertain the hel out of me)
And silverentrantress, that article is great!
I just read through it, and the guy says many of the same things I said here, simply in a more flowery manner. He also elaborates onto subjects I didn't go into.
Overall... excellent article, and VERY true to how I've experienced things.
Especially the bits about the differences in our language usage.