Will fresh strawberries make a cake soggy?
I also think that the strawberries won't be much of a problem. But if you use lots of them, or if they are frozen, or if you want to use other, moister, fruit in the future, you could run into problems. And you would be relieved that there is a solution. 

The solution against cake getting soggy from fruit is to simply seal the cake layers against moisture. The traditional way is to glaze with apricot jam - you brush a very thin layer of melted apricot jam on the cake layer, and put the fruit on it after it has cooled. The amount is so small that the taste is not noticeable, and it is also practically invisible. Alternatively, you can use other glazes, such as slightly thickened simple syrup (cooled, so it won't seep into the layer itself), starch cooked in water (evtl. with some sugar), other jams, or commercially available sealers (Dr Oetker sells them in sachets).