I found old plans for a quagi that uses copper for the Reflector and Driven Element and any 1/8" metal available for the directors. The general recommendation for antennas is: no steel for the DE. Is it OK to use for the directors, and OK to 'mix' the metals in an antenna? I'm very new to building and ham in general. I might be able to find something besides steel but so far everything non-steel around here is larger than 1/8".
It's probably OK to use a different metal for the directors than the driven element, as long as you don't have dissimilar metals touching that would create a galvanic corrosion problem. But steel is a lousy conductor that would make your antenna less efficient. If you wanted to know exactly how much less efficient, then you could model the antenna in EZNEC or 4nec2 to find out.
If you're just making an antenna to better reach the local repeater, and you're not concerned with every decibel, then go ahead and try it! If you're intention is to use the antenna for moonbounce work, in which case you would be concerned with each and every dB, then you're probably better off finding copper, brass, or aluminum rods to use for the directors rather than steel.
My guess would be that the 1/8" diameter recommendation reflects what the antenna designers had on hand; I wouldn't think that a larger diameter would change the specifications of the antenna much. I don't have much experience building VHF/UHF yagis though.