I have a few clients with this dilemma, the thing is to us to us ordinary dull mousey blonde humans! The thought of having fabulous strawberry blonde hair naturally would be a thrill. So the first thing I would suggest is to stop messing around trying to cover up or get rid of what nature has given you, beautiful strawberry blonde hair, did you know itís the most difficult colour for us professionals to re create with out the colour fading out rapidly! So I would suggest that you build the condition of your hair up so that your hair reflects the light and shines, have a great hair cut and go au natural.
If however reading that option you are now pulling your hair out!
You could do the following, but you must know the rules of having a strong red tone in your hair naturally.
If you are going to darken it have it done by a professional as because you have been bleaching your hair with various lightening products, you could have incompatible deposits on your hair and these could react making your hair in poor condition, change to a horrid khaki colour or chemically disintegrate. So incompatibility tests must be done. If you go darker but use a permanent tint to do so, after a few shampoos the red in your hair will still show through, as the hydrogen peroxide in the perminant tint mixture will expose the red tones that are in your hair. I would recommend a long lasting semi permanent colour that has a very low level of oxidant that will not expose the hairs natural red ( like a Diacolor richesse from LOreal) This will last for several shampoos, but be careful it may grab on the bleached up hair.
If you are going to be going lighter then, unless you are going to bleach the hair up to as pale as you can go and tone it, then use ash shampoos, (all of which I would recommend a short hair cut to maintain the condition) This is high maintenance hair coloring and for it to last and look good, your looking at 2 weekly root application and to replace the ash tone which will wash off exposing the red again. (This may also be too light for your skin tone leaving you looking sick.) Highlights wont work as it only picks up a % of the hair and the rest will remain red.So your are much better off, will have less stress in your life if you accept what nature intended and have the strawberry blonde that you have with more red tones to make it look shinny, textured and healthy.