This is a really tough question to ask, because it all depends on what you define as "strong"(I'm a mechanical engineer). Titanium is strong for how much it weighs, but is inferior to steel in a lot of ways as well.
I guess the best answer I can give you is to simply define what you mean by strong.
If its volumetric strength(e.g. strength per unit of volume) titanium gets its ass wooped by steel(due to its elastic modulus and ability to be hardened). In other words, where weight isn't a big factor, always use steel. A sword made of steel will be far stronger than an equivalent sword made of titanium(not to mention steel can be better crafted to specific levels of hardness for edge retention) because a 1/2" thick bar of steel will be far stronger than a 1/2" thick bar of titanium. So if size(as opposed to weight) is a factor, steel is a solid choice.
If weight is a factor, then you're left with carbon fiber, aluminum, magnesium, and titanium alloys. These each also have the same issue as above, in that for a given volume they're all inferior steel. Of these, titanium is probably the all around best material, simply because it's isotropic(just as strong being squeezed together as pulled apart unlike carbon fiber), and has a high melting temperature as well as an endurance limit(means it can be engineered to basically never fail as long as loads don't exceed a certain limit, the other materials will eventually fail to a falling hair after enough repeated loads). However titanium is also stupidly expensive compared to a quality aluminum alloy, and magnesium sort of straddles the middleground between aluminum and titanium. Carbon fiber is a good material, BUT it's difficult to work with structurally because of it only be strong in tension, it's absolutely worthless if put under a shearing load and it's pricey.
If heat is a big factor, then you're looking at a material like tungsten, that loses very little strength as the temperature increases, and it can withstand VERY high temperatures.
If corrosion is a factor, stainless steel is a solid choice, titanium is great, but the ultimate matiral is iridium or the other noble metals(gold, platinum, etc.). Iridium is the shit, and is immune to just about anything you could throw at it, but it also costs thousands of dollars an ounce, so it's typically only used in special circumstances.
If I were going to pick an all around material, I'd go with a quality steel(stainless if corrosion is an issue). Steel alloys exist that range from the super hard tool steels, to the soft nearly carbon free steels. Also a large variety of different strength and weight properties means that somewhere there's probably a steel that exists that is tailor made for the job. Not to mention that steel is pretty affordable and readily available.