How to claim counties of my duchy?

Actually there a number of significant advantages of the ducal title itself. As a lowly count, given a choice of having the title or having the de jure counties without the title, I'd rather have the title.

Here a list of advantages of being a duke over a count that come from the title itself.

Better Marriage Prospects

As a relative of duke your sons and daughters will have a significantly larger pool of a potential spouses. You'll be able to marry them off to off to characters with better attributes and better claims. You can gain better alliances, and maybe even bring a new title into your dynasty. In a game about building your dynasty, arguably better marriage prospects is the biggest single advantage of holding a ducal title.

Counts as Vassals

The penalties for going over your demesne limit are fairly severe, and as count there's not a lot you can do about it. As a duke you can give away your extra counties to (hopefully) loyal family members. Once you're no longer over your demesne limit you can scheme to add even more counties to your realm without having to worry about making a bad problem even worse. Being a duke lets you have a bigger, richer, and more powerful realm than you could have as a mere count.

Prestige

A duke title gives twice as much a prestige as county title. Your vassal's titles also give you prestige, the same as if you held the titles yourself. Given that your realm can now be bigger and include counts as vassals this means you can earn more prestige as a duke than you can as a count. Having more prestige makes things generally easier. Other nobles will like you more, and can spend it to fabricate claims and other actions. Having a ducal title is also worth twice a much as county title to your dynasty's prestige, which determines the prestige every member your dynasty is born with.

Permanent Casus Belli

Sure you can't go to war over the duchy's de jure counties right now, but there's no hurry. As long as you hold the title you'll still have a claim and there's no big advantage to controlling county in your duchy over one outside of it. This means that you can look for other easier to acquire counties to add to your realm, and safely put off gaining control of the de jure counties for later. For example, if your current king is both popular and powerful, you can patiently wait for a weaker king to come to the throne before trying to lower the crown authority. In the mean time you can turn your attention to any weak claims you can press or claims that will expire when you die.

Electorship

If your de jure kingdom (and/or empire) uses feudal elective succession then as a duke you now get to vote on who gets to be the next ruler. If it's not currently the succession law you now have a reason to form or join a faction to change it to feudal elective. Even if you aren't able gain enough support right away to put yourself on the throne, you may get to cast the deciding vote between a powerful new ruler and a weak and ineffective one.

Synergies

The first three advantages all synergize with each other. Better marriage prospects gives you more options expand your realm, allows you to marry into more prestigious families and can put more titles into your family tree. More vassals means more prestige for you and if you install family members, for your dynasty as well. More prestige means your vassals will like you more and other rulers will be more likely to agree your marriage proposals.

Simply put becoming a duke means that you've climbed up a rung in the ladder. It's far from a meaningless title without its de jure counties, so you shouldn't be disappointed. Your now in a much better position to expand your realm and your dynasty than you would have been if you just gotten the counties. You're also in a much better position to ultimately take control of the kingdom, whether by marriage, war or election. This all true even if you never gain control of any of your duchy's de jure counties.