Antenna height is the biggy when talking about dipole directionality. Even at a wave length, there won't be huge gobs of that directionality, but the radiation pattern will -tend- to be at right angles to the antenna, the lesser amount off of the ends of the thing. Those 'nulls' are also sort of misleading, there's still signal being radiated, just not as much as off of the 'sides'. At lower heights the radiation pattern tends to be omnidirectional. Maybe a 'wide oval' sort of shape as the antenna nears that 1 wave length height.
None of those radiation patterns are ever going to be as 'regular' or nicely shaped as the classical examples you see in books/web sites. Anything/everything around that antenna is going to have some affect on that radiation pattern's shape. Probably not much, but it can get sort of weird looking.
Inverted 'V' antennas are still a typical 1/2 wave dipole. They act like one, and very seldom get very directional. That's mainly because they are typically used because of limited space. The biggest benefit to them is that "less space" to put them up in, and the angle between the legs of them does contribute to an impedance match to 50 ohms. As the angle between those legs get's smaller, the input impedance drops from a typical 70-75 ohms to something closer to 50 ohms. Varying that 'angle of the dangle' is one way of adjusting impedance matching without affecting resonance too much.
If you want a single multiband antenna then the two things that will affect things the most is the overall length and what you use for a feed line. A center fed doublet at the lowest band of interest will typically work on the 'odd' harmonically related bands (not so good on the 'even' harmonics) -higher- in frequency from the primary band of resonance. That just means that the 'bigger the better' to some ridiculous extent.
The two most common feed lines used are coax and 'ladder-line'. Each have their pluses and minuses. The biggy is that ladder-line can withstand a much higher SWR before it's affected much. Coax has a much smaller SWR 'range' before it's damaged. Use the one that's least affected by being off frequency for the best results. Depending on the non-resonant frequency, the input impedance can be all over the place! So, using a tuner at the transmitter end is very common. The 'limit' to that is the amount of 'system' impedance mismatch the tuner can handle, AND the amount of SWR the feed line can withstand without being destroyed. Of the two types, coax and ladder-line, the ladder-line will win that 'game' every time. While having a multiband single antenna is 'good' (fewer antennas) you also have to keep in mind that it's radiation pattern will change drastically with each band change. It will radiate a signal, but there's really no predicting where/how that signal will go without modeling the thing with every variable accounted for. If you are 'happy' with where/how the thing performs, good. If not, then change it's shape or positioning. How do you tell? Try it and see!
All of the above are generalizations, nothing real specific.
- 'Doc