With the loose neutral connection is this esentally beause there will be a voltage drop between the neutral in the panel and the transformer neutral which is grounded? Therefore is the neutral is bonded to ground in your panel and you touch something that is bonded to the ground then there will be a potential difference between the ground and earth?
Yes, you have the idea. Loose neutral will normally show up in other ways to, such as lights being bright on one circuit and dim on another or as you turn loads off and on you will see this. Under the worst conditions your electronics will let the smoke out. Don't use your hands to test for voltage as look for the problem. It could be lethal under the right conditions.
As kwired has stated you do need to find out what is elevated in voltage. It could be a POCO problem. Put your meter between the offending contacts, floor & faucet, faucet & drain, or whatever. Shut things off in the house and watch what happens. Once everything is off and if you still have voltage it is most likely outside the home.
Once you find the problem, go back and bond everything correctly.