First of all, when you read about a "50W LED", it is certainly saying that it outputs the equivalent light of a 50W incandescent light (although that is often a exaggeration). That "50W" LED actually draws less than 10 watts. This means that it draws much less current and emits much less heat, both of which are the factors that typically limit the allowable light in a fixture.
You'd be able to replace a 50/100/150W 3-way with a lower wattage, even if staying with incandescent.
Second, unless the LED light is marked "dimmable", don't try to use it on a dimmer. You may damage the dimmer, light, or both. Even if the light is dimmable, some dimmers will not work well with a low load: a dimmer that works on a 100W light bulb may not work on an equivalent-light-output 13W LED. They make LED/CFL specific dimmers that may work better.
As for the 130V R40, that is probably a "long life" bulb. Running an incandescent at lower than rated voltage extends its life. Therefore, they make 130V bulbs to run longer on 120V. Just use LEDs rated for 120V.
As for your existing florescent lighting, I assume you're talking about the straight tube type. For a fixture that old, it's probably less efficient that newer florescent fixtures or LEDs but still much more efficient than incandescent. This is harder to replace with LEDs, just due to the area covered. There are LED tubes made to replace florescent tubes but they are still expensive and generally require re-wiring the fixture. These are most often used in commercial applications.
The wattage ratings are typically listed to reduce possibility of excess /heat/ buildup in the fixture. If you want to use 3x 60 watt bulbs, consider replacing traditional incandescent bulbs with newer CFL (spiral) or LED bulbs. Either choice will use much less electricity and also emit much less heat, staying within the safety rating for the fixture.
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Are these on a dimmer, perhaps? Dimmable LEDs need an LED-rated dimmer to be happy, generally. If the dimmer is old that usually means replacing it.
You have not increased the wattage. The Wattage is 15W per bulb - the "equivalent wattage" is marketing organic fertilizer meant to convey the lumen output relative to an incandescent bulb. It has nothing to do with actual wattage.
You may have an issue where the base of the bulb is too fat, too soon for the fixture socket, so that no contact is being made to the center contact. Depending on how extreme this is it can sometimes be helped (circuit breaker for the circuit OFF, please) by gently, slightly, bending the center contact in the socket up just a bit - but if you overdo it you can snap the contact off, so don't overdo it.