Care must be taken when staining birch, which tends to blotch easily. It takes some research and a bit of experience to get it right. Water-based dye stains, gel stains, alcohol dye stains, or a prepping agent for oil-based stains are generally required. You can probably correct the problem, but it is going to be challenging.
A little Internet research will tell you what you need to know, but here are a couple quick links:
http://www.askthebuilder.com/497_Con...Staining.shtml
http://research.the-bac.edu/color/wood/
From the last link above:
How To Prevent Blotching
Some woods, such as walnut or oak, tend to color evenly. Others, such as cherry, maple, birch, or pine, are harder to manage. The reason why some woods color unevenly (known as blotching) and others don’t is widely debated. Some say that the culprit is swirled grain, while others attribute it to resin pockets that occur during kiln-drying. However, as far as the coloring of wood is concerned, all of the possible reasons for blotching are irrelevant. This must always be dealt with regardless of its cause.
Certain products on the market, or methods used while staining, can alleviate this condition (but most have limitations):
* If an oil-based color or varnish is being used, a stain controlling solution may prove to be useful. This solution will absorb into the blotchier areas of wooden surfaces, but is not compatible with other stains: water-based, alcohol, or lacquer.
* The consistency of the stain being used also impacts the outcome. Gel stains do not easily penetrate the wood, hence the color looks better than on a stain-controlled surface. Although both water and solvent-based gels are available, they also do not entirely guarantee blotch-free staining.
* A lesser known process known as glue-sizing is sometimes advocated to control stain penetration. Glue thinned to liquid at room temperature is absorbed and dried into the wood before sanding. The resulting layer of glue and wood acts as a partial sealer to prevent blotching.
When dealing with the surfaces that tend to absorb color unevenly, the following key points must be kept in mind:
1. Control the depth of penetration as much as possible.
2. Remember to keep the color close to the surface.
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P.S. At this point, I would probably seriously consider painting and applying several (5 to 8) coats of finish to create a high-gloss lacquer look. I personally never stain birch, maple, or pine for the above reason. Some people do it and it looks fine, but I think it's more trouble than it's worth. See my sig for woodworking samples from my own shop.
