The summoned creature is a valid target of such effects however it has no inherent ability to use basic attacks so the end result is not favorable for you.
The attacks allowed to each summoned creature are as listed for each power. Currently I am aware of none that grant basic attacks. Summoned creatures are not granted any basic attacks by default. Basic attacks are indicated like this 
for Melee basic attacks and like this 
for Ranged basic attacks.
The Rules Compendium states on p120 in the Commanding the Creature section that, "The Summoned Creature has no actions of its own...The Summoning power determines the special commands that the summoned creature can receive and gives an action type for each command."
Compare Basic Attacks to Opportunity Attacks.
Opportunity Attacks, like Basic Attacks (as Simon notes) are also granted to all creatures (RC p246). There are many summoned creatures that are explicitly granted Opportunity attacks. See Phantasmist Stalker for one example, its Opportunity Attack is identical to its normal attack.
From this you can infer that Summoned Creatures do not have Opportunity Attacks by default. Hence they should have no Basic Attacks as well.
Summoned creatures are not real creatures.
It's important to notice that a summoning is not a calling. Although they are both from the Conjuration school, you do not summon a specific creature, you summon a generic specimen of that creature type. The summoned creature cannot be summoned again until 24 hours is passed, while it reforms itself on another plane.
Conjuration
Each conjuration spell belongs to one of five subschools. Conjurations transport creatures from another plane of existence to your plane (calling); create objects or effects on the spot (creation); heal (healing); bring manifestations of objects, creatures, or forms of energy to you (summoning); or transport creatures or objects over great distances (teleportation). Creatures you conjure usually- but not always- obey your commands
As we can see here, the main difference between a calling and a summoning is that one transports a creature, while the other brings a manifestation of a creature.
We then see further differences between the two types of conjuration, specifically about the manifestation reforming or the creature dying if killed.
Calling: a calling spell transports a creature from another plane to the plane you are on. The spell grants the creature the one-time ability to return to its plane of origin, although the spell may limit the circumstances under which this is possible. Creatures who are called actually die when they are killed; they do not disappear and reform, as do those brought by a summoning spell (see below). The duration of a calling spell is instantaneous, which means that the called creature can't be dispelled.
Summoning: a summoning spell instantly brings a creature or object to a place you designate. When the spell ends or is dispelled, a summoned creature is instantly sent back to where it came from, but a summoned object is not sent back unless the spell description specifically indicates this. A summoned creature also goes away if it is killed or if its hit points drop to 0 or lower, but it is not really dead. It takes 24 hours for the creature to reform, during which time it can't be summoned again.
When the spell that summoned a creature ends and the creature disappears, all the spells it has cast expire. A summoned creature cannot use any innate summoning abilities it may have.
We can tell that the rules are a little vague about this. But James Jacobs also seems to support the idea that summoned creatures are not real, but manifestations based on real creatures.
Commune Spell-like Ability from Summoned Creatures
If the creature was summoned via Summon Monster spell, it says this on the spell effect:
Creatures summoned using this spell cannot use spells or spell-like abilities that duplicate spells with expensive material components (such as wish).
We can see on the spell text of Commune that it does have an expensive material component, thus summoned creatures cannot use their Commune spell-like ability. This is because summoning spells do not allow it, not because the creature may or may not have used it this week.
Components V, S, M (holy or unholy water and incense worth 500 gp), DF
For spells without components, the monster should have all their spell-like abilities available when summoned.
It's possible that there exist Conjuration(Summoning) spells that are not copies of the Summon Monster spell, and those, if their spell text does not say functions like Summon Monster or does not forbid the use of expensive spells, should allow their use. But, as far as I know, no such spells exist. All spells that summon specific creatures, such as Summon Genie or Summon Thanadaemon, also specify that they work like Summon Monster.
There are a few spells that are a Conjuration(Summoning), but does not have the expensive material clause, such as:
Conjuration(Calling) Spells
Calling spells are a whole new deal and allow you to use their spell-like abilities, if that's part of the contract, in some cases, and if the creature likes you enough, in others.
Spells like Plannar Ally, Gate and Planar Binding will conjure real creatures, with names and personalities, and should have all their abilities on their stat blocks available. They might also have things not listed on their bestiary (or source book) such as different equipment (axes instead of swords), different personalities (a neutral succubus?), different feats and skills, and even different classes since many of those creatures are intelligent enough to take class levels.
Example: a conjured Imp can use his Commune spell-like ability.
There might be exceptions to this, but this is the general ruling for calling spells as they have nothing that prevents them from using their spell-like abilities.
But be warned to not abuse those creatures when you conjure them, as you could make terrible enemies that will remember everything you have done to them while they were under your control.
Best Answer
There is no easy answer
This is a tough situation and the solutions are all generally things that can make players feel that their strategies are being specifically targeted. That doesn't leave you with a lot of options for how to address, but here are some considerations in evaluating what to do.
Talk it out
As has been discussed, talk about what's happening with the players. Managing so many creatures isn't fun for you, and that's totally reasonable. Let them know it's a cool tactic and can be used, but please don't use it all the time. Chat about what they like about it, what concerns you, and at least see if they can understand where your coming from and see if they'll choose to alter their strategies.
I had played a bard for awhile that used animate objects and it honestly got tiring for me, too. And it seemed too much, so I only used it when it really made sense to use it.
Summoning is tricky, the DM technically picks
Going by pure RAW, the character's aren't picking the creatures, the DM does. But honestly, that's not a lot of fun. I don't think I've played at a table where the DM has picked the summoned creatures. Using this in your discussion may be a reasonable tactic to show that if you wanted to press the rules-first approach, then you could allow them to summon, but that you choose (maybe randomly) the creatures. That limits the capability within the rules, but it definitely isn't quite the same fun/feeling for the players.
Nerfing the spells
I'm really not a fan of this, especially if the strategy and use is by the book (which it kinda isn't with the above, but you get the point.) Taking away toys because you don't like it can present it's own table issues. There are better ways to handle this.
Encounter design
This ultimately is most likely your biggest lever here. While you don't want to create every encounter that counters this strategy, it isn't crazy to start filtering them and also having the minions of the BBEG know the strategy to counter it.
Counters
The most obvious here is going to be bringing in monsters that are resistant or immune to mundane damage. Summoned creatures aren't usually dealing damage that bypasses magical damage resistance or immunity, so bringing monsters in with those traits nullifies the summoned creatures strategy.
Next up is area affect attacks. These summoned creatures generally also don't have a lot of HP (especially the tiny animate objects). Drop an AOE on the, and you'll wipe them out.
Environment design can also play a part here. Make it so it's difficult to maneuver or have room for the summoned creatures and the option to summon them gets taken off the table.
Keep everything as-is, but introduce Handling Mobs
Chapter 8 of the DMG (Thanks goodguy5!) offers some optional rules around Handling Mobs:
I haven't personally used this before and, as always, talk to your players about it. This isn't about you as the DM using this for your monsters, but minimizing the player interaction with their summons. This may not be what they're looking for.
But having fun is the key
Balancing letting your players use the tactic they enjoy with challenging them and yourself is the name of the game. Let them shine, but also put them in situations where their go-to strategy isn't an option. Coming up with new strategies and working out how to handle an encounter differently can be fun, too.