Why did someone misadjust the transformers? - it's something you NEVER need to touch.
You're probably fine adjusting it just using a radio station - however, you've no idea what actual frequency you're adjusting it to, that's why you're supposed to use a signal generator. Use a weak radio station though.
A scope is of little use, as the signals are really VERY low, and a meter is of course useless.
What you could use, is an analogue meter on the AGC line, which gives you an accurate representation of the signal strength - a digital meter is pretty poor for doing this though.