Hello,
The Head stock bearing have gone tight, I take it it feels like it doesn't wish to steer when you do and then suddenly you have steered tooooo much. You can try loosening them, a bit if this is possible or you may just need to replace, a bit of oil into the bearings will most likely cure the problem as well. Lube the bearings from the top and bottom you may have to turn the bike upside down to do this.
The chances are using it in the rain has slowly washed the lube from the bearings, the oil thing should save you if they haven't go to far or at least improve the steering a little.
Really you should strip the thing and regrease if the bearings seem OK as the oil will get washed out quite quickly in wet weather but it will at least prove if the problem is caused by this.