The strongest element is probably Tungsten. Tungsten is very strong at room temperature, but also maintains its strength at much higher temperatures without softening. However, ranking the strongest elements is not a simple task, due to complicating factors.

The ultimate tensile strength of a material tells us about how strong it is. It is measured in units of force per unit area, e.g. mega- Newtons per square meter, which is a mega-Pascal (MPa). Tungsten has a tensile strength of ~980 MPa (1862 MPa when cold worked). The ultimate tensile strength is the amount of stress the material can withstand while being stretched before breaking.

Various treatments can be used to increase the strength of a material, so the strength of an element can vary significantly depending on how it was formed into its current shape. One example of a process that is used to strengthen materials is work hardening (or cold working). There are many ways to do this, but the general idea is that the crystal grain structure in the material can be changed by plastically deforming the metal and introducing defects. While it does make the material stronger, it also makes it less ductile and more brittle. Another process that changes the strength of a material is heat treating, which can increase or decrease strength depending on how it is done and which material is used. One example is quenching, which is a process where the material is heated and then rapidly cooled. The important point here is that strength depends on the microstructure of a material so two different samples of the same pure element can easily have very different mechanical properties and very different strengths.

The strength of a material also greatly depends on the purity of the material. Alloys of two or more elements can produce a material that is much stronger than any of the pure elements. So for example, pure iron has a tensile strength of ~350 MPa but if you add a small amount of carbon (<1%) to it, it becomes steel and with heat treating, its strength can increases to ~840 MPa. The strongest treated alloys can reach 4000-5000 MPa.

Strength alone is not the only important property of a material. Depending on the application, toughness, hardness, ductility, weight, cost, or reactivity, etc may be important. The alloy, stainless steel, is important in many applications because it is less reactive (more resistant to rust) than iron and other steels. Titanium and titanium alloys have a high strength to weight ratio. Even though they are not the absolutely strongest materials available, titanium alloys are very important in applications like aerospace where weight is an issue.

References:
material group
crcnetbase
wikipedia

Your question is hard to answer because different people have different ideas about what strong is, especially when related to elements. Even for materials, where "strong" might be a more commonly used term, it does not have a very rigorous definition and therefore can lead to confusion. Just consider the famous example of spider silk, which is frequently called "stronger than steel" (which we might intuitively understand as being able to sustain a given weight at a lower weight of the suspending "string"), but it also happens to be viscoelastic (similar to silly putty) meaning that spider silk could not be used to, say, build bridge cables.

So it turns out that there are many material properties that are connected to "strength" of a material, and often one must find a balance between them. Very hard materials such as ceramics, for example, can often also be quite brittle, which may limit their usefulness. I chose hardness as an example because your question was about elements. You may already know that diamond is the hardest material, and diamond is a form of the element carbon. Not the only form, and another (much more common) form of carbon, graphite, is very soft. Elements are the basic chemical entities: materials and molecules are made up from atoms, of which there are around 100 different kinds or elements. What atoms make up a material and the way they are connected (as in the example of diamond versus graphite) determines the properties of the material on the molecular scale. There are many additional factors that affect the larger-scale (e.g. at sizes visible to the naked eye) properties of a material, and often materials are combined at that scale to improve on their individual properties. An example is reinforced concrete, where the steel grid inside the concrete greatly improves the overall "strength" of the material. Other materials such as wood and fiberglass work by the same principle.

Hope that this, while not exactly an answer to your question, is some food for thought and can fuel your curiosity!