Is there a way to make a very strong pickaxe?

Well, you need to have enough XP (killing mobs, mining ore, smelting ore, etc.), and you will also need Lapis Lazuli in order to make better items at an enchanting table. Using book shelves at least a block space away from the enchanting table (with nothing in the way, no torches, nothing) will power it more. You might also want to find enchanting books, which can be found by fishing, or by searching chests underground (more chances of finding it in strongholds). If you want to use an enchanting book use an anvil to combine the book with your tool. The strongest type of pickaxe is the diamond pickaxe, which can be crafted by diamonds. Diamonds can be found deep underground starting below layer 16 (best chance in layer 11). It can only be mined with at least an iron pickaxe.

There are several ways to obtain the enchantments you're looking for:

1. Fishing - this is random, and there is no guarantee that you can find what you're looking for. However with a Fishing rod with Luck of the Sea and Lure, you should hopefully be able to find some useful items.

2. Grinding - i.e. the usual method. This can be broken down into several steps, or different approaches. However, it can get quite expensive, and you may not be able to achieve this, once the cost gets too high.

   • Books: Enchanting books is the "cheapest" method, though it will take some time and a lot of resources to craft the books, and enchant them. There is no guarantee you'll be able to get what you want. Once you have 2 books of the same level enchantment (i.e. Unbreaking 1); you can combine them in the anvil to make an enchanted book of a higher level. This can get quite expensive and time consuming however, as to increase the enchantment again, you will need two books of the same level (Unbreaking 2 x 2; which means you will need 4 Unbreaking 1 books. This grows exponentially).
   • Gold Tools: Using gold tools is another method of "tricking" the enchantment table into giving you better enchantments for your weapons/tools. By placing a Gold Pickaxe in the table first, you have a higher chance of getting more powerful enchantments, which you can then remove from the table, put in your Diamond Pickaxe, and apply an enchantment that way. While less time consuming, this is entirely random, and you will have no control over the enchantments you do receive on the equipment*.

As for the Diamond Pick, you can mine diamonds normally, using either an Iron or Diamond Pickaxe. I would refrain from using a Diamond Pickaxe however - this will incur a cost to repair, and may get too expensive to enchant. Iron is fairly common and inexpensive, and will do the job well enough until you collect the resources for enchanting your Diamond Pick. Diamonds can be found around levels 16 to 5

^{*There is a belief that the "enchantment language" can be translated, to identify which enchantments are currently on offer. However, I personally do not believe this to be true.}