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Damn straight the research is all over the map, and the field is awash in factoids, disputing gurus, and pundits grinding axes. I expect our 'enthusiastic' posters are shortly going to be sharing many of them with us.
You can account for the high numbers of females hitting men by looking at the definition of "hit" or "violence." You get it broad enough, a playful slug in the shoulder gets counted. (Early in our relationship, I had to sit down with the spousal unit and explain that even though I was a largish athelete, I was not a Gumby doll and it did in fact hurt, even if I acted all manly about it, and could she please stop? She did. But I suppose I could be counted as a male "victim.") There is also the factor that women are going to be a lot less ashamed to self-report than men are.
On the other end, you can account for the violence causing injury statistics being so much higher in women because a) as other posters have pointed out, there is a size/strength differential, and b) once again, women these days are much more likely to tell hospital personnel the truth. Similarly with crime stats.
In my professional experience, I most certainly see women getting damaged rather more often than men, and needing to flee the house. I have seen no signs of an epidemic of husband battering, but it does happen. We are specifically funded to provide shelter for men and their children fleeing abuse; in the last four years not one single request has come in, while at the same time the secure women's shelters are packed. I don't think that this indicates it doesn't happen, my guess is that men tend to have more resources to fall back on and don't need it.
In terms of psychological abuse, my sense is that women have the upper hand there, what with better verbal and social skills, so the victimizers are probably women somewhat more often than men. But just try and come up with a concrete definition of psychological abuse, usable in a research context.
Interestingly, domestic violence & abuse seems to occur at almost the same rate in same-sex relationships of both genders, though somewhat less often than with het couples. The lower likelihood of children in family tends to make it a good deal easier for a victim to flee I suspect, that and there being less social/family pressure to "keep the family together."